Education 1966–1973: Student of Physical Technical Faculty, Tomsk Polytechnical
University, graduated with honour diploma 1973;
1973–1976: Postgraduate (aspirant), Tomsk State University
Promotion: Ph D in Theor. Phys., awarded by Voronezh State University, 1978
(Thesis "Separation of variables in relativistic equations of quantum theory and explicit solutions under Bagrov V.G., readers — Prof. Shabad A.E. and Prof. Loskutov Yu.M.).
D Sci in Theor. Phys., awarded by B.I. Stepanov Institute of Physics, the National Academy of Sciences of Belarus, Minsk, URSS, 1990
(Thesis "Symmetry Problems in Basic Equations of Field Theory readers — Prof. Kaigorodov V.R., Prof. Mir-Kasimov R.A., and Prof. Khalilov$nbsp;V.R.)
Areas of expertise: Theory of separation of variables in equations of mathematical physics;
Symmetry analysis of equations of mathematical physics; Soliton theory and its applications to nonlinear waves in DNA; Dynamical models of biological populations, dynamical chaos
Semiclassical integrability of nonlinear equations of mathematical physics; Reaction-diffusion equations
Employment: 1978 — present: Assistant Professor (1978–1982), Associate Professor (1982–1992),
Full Professor (1993–1996), Head of the Chair of Theoretical Physics Department
(1996–present)
Physics Faculty, Tomsk State University,
2000–present: Professor, Mathematical Physics Department, Tomsk Polytechnical University
Teaching experience: 62 Semesters at the university level; PhD adviser: 11 Ph D students (aspirants) have got the degree
DSci adviser: 3 Sci D postdoctorants (doctorants) have got the Sci Doc degree
Main lecture courses: Theoretical Physics (for students of Mechanical and Mathematical Faculty); for students of Physical Faculty: Electrodynamics, Quantum Mechanics, Nonlinear
Equations of Mathematical Physics, Functional Analysis, Theory of Finite Groups, Asymptotical methods, Introduction to the Theory of Fractal Structures, Symmetry of Differential Equations, Integrable Systems;
for students of Mathematical Economy (Tomsk Polytechnical University): Differential Equations
in Economy, Mathematical Models in Economy
Research grants Russian Basic Research Foundation (1998–1999,2000–2001)
Fundamental Research Programme of Russian Ministry of Education (1994–1995, 2001–2002),
Russian Human Research Foundation (2004–2006)(collaboration)
Grant of President of Russian Federation (2003–2005, 2006–2007, 2008–2009)(collaboration)
Analytical Research Programme of Russian Ministry of Education and Science
(2009–2010)
Federal Research programme of Russian Science and Innovations Federal Agency
(2009–2011)(collaboration)
A. V. Shapovalov, S. E. Siniukov, Quasiparticle solutions to the 1D nonlocal Fisher–KPP equation with a fractal time derivative in the weak diffusion approximation, 2025 , 26 pp., arXiv: math-ph/2503.15099
A. I. Breev, K. V. Vasilev, A. V. Shapovalov, “Rasshirenie simmetrii i obobschennye invariantno-gruppovye resheniya uravneniya teploprovodnosti i uravneniya Byurgersa”, Izvestiya vuzov. Fizika, 67:1 (2024), 99–108
4.
A. E. Kulagin, A. V. Shapovalov, “Kvaziklassicheskie kvazichastitsy dlya uravneniya Shredingera s nelokalnoi nelineinostyu i antiermitovoi chastyu”, Voronezhskaya zimnyaya matematicheskaya shkola S.G. Kreina – 2024 : materialy mezhdunarodnoi Voronezhskoi zimnei matematicheskoi shkoly, posvyaschennoi pamyati V. P. Maslova. (Voronezh, 26–30 yanvarya 2024 g.), 317 c. ISBN 978–5–9273–3692–0, Izdatelskii dom VGU, Voronezh, 2024, s. 130–132https://vzms.kmm-vsu.ru/files/vzms_2024.pdf
5.
A. E. Kulagin, A. V. Shapovalov, “A semiclassical approach to the nonlocal nonlinear Schrodinger equation with a non-Hermitian term”, Mathermatics, 12:4 (2024), 580 , 22 pp. https://www.mdpi.com/2227-7390/12/4/580, arXiv: 2308.08286
A. V. Shapovalov, A. E. Kulagin, S. A. Sinyukov, “Nevyazka kvaziklassicheski sosredotochennykh reshenii kineticheskogo
uravneniya na primere nelokalnoi modeli ionizatsii aktivnoi sredy”, Izvestiya vuzov. Fizika, 67:2 (2024), 36–44
V. V. Obukhov, K. E. Osetrin, A. V. Shapovalov, “Comments on the article 'M.O. Katanaev, Complete separation of variables in the geodesic Hamilton-Jacobi equation in four dimensions, Physica Scripta (2023), 98, 104001'”, Physica Scripta, 99:6 (2024), 067002 , 4 pp.
9.
S. A. Sinyukov, A. E. Kulagin, A. V. Shapovalov, “Dinamicheskaya sistema momentov dlya nelokalnogo uravneniya Fishera – Kolmogorova – Petrovskogo – Piskunova s drobnoi proizvodnoi po vremeni v priblizhenii slaboi diffuzii”, Izvestiya vuzov. Fizika, 67:8 (2024), 5–14
10.
A. V. Shapovalov, S. A. Siniukov, “Fractal dynamics of solution moments for the KPP–Fisher equation”, Russian Physics Journal, 67 (2024), 1827–1837
2023
11.
A. V. Shapovalov, A. I. Breev, “Harmonic Oscillator Coherent States from the Standpoint of Orbit Theory”, Symmetry, 15:2 (2023), 282 , 11 pp., arXiv: quant-ph/2211.11029
A. E. Kulagin, A. V. Shapovalov, “Analytical description of the diffusion in a cellular automaton with the Margolus neighbourhood in terms of the two-dimensional Markov chain”, Mathermatics, 11:3 (2023), 584 , 18 pp. https://www.mdpi.com/2227-7390/11/3/584, arXiv: 2208.03014v2 [math.PR]
A. V. Shapovalov, “On equivalence between kinetic equations and geodesic equations in spaces with affine connection”, Symmetry, 15:4 (2023), 905 , 16 pp. https://www.mdpi.com/2073-8994/15/4/905
V. N. Zadorozhnyi, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast III. Differentsialnoe i integralnoe ischislenie. Chast III. 4. Integralnoe ischislenie funktsii neskolkikh peremennykh, v. III, Integralnoe ischislenie funktsii neskolkikh peremennykh., eds. prof. V. Ya. Epp, prof. V. N. Cherepanov, Izd-vo TPU, Tomsk, 2023 , 502 pp.
A. V. Shapovalov, A. E. Kulagin, S. A. Siniukov, “Family of asymptotic solutions to the two-dimensional kinetic equation with a nonlocal cubic nonlinearity”, Symmetry, 14:3 (2022), 577 , 20 pp., arXiv: math-ph/2203.02333
T. V. Gandzha, K. A. Isakov, A. V. Shapovalov, “Analysis of the kinetic model of a single-stage process for obtaining titanium dioxide”, Russian Physics Journal, 65:4 (2022), 663–670https://link.springer.com/article/10.1007/s11182-022-02682-6
18.
A. V. Shapovalov, A. E. Kulagin, S. A. Siniukov, “Pattern formation in a nonlocal Fisher–Kolmogorov–Petrovsky–Piskunov model and in a nonlocal model of the kinetics of an metal vapor active medium”, Russian Physics Journal, 65:4 (2022), 695–702https://link.springer.com/article/10.1007/s11182-022-02687-1
A. V. Shapovalov, R. Brons, “Invariance properties of the one-dimensional diffusion equiation with a fractal time derivative”, Russian Physics Journal, 64:4 (2021), 704–716
21.
A. E. Kulagin, A. V. Shapovalov, A. Yu. Trifonov, “Semiclassical spectral series localized on a curve for the GrossPitaveskii equation with a nonlocal interaction”, Symmetry, 13:7 (2021), 1289 , 22 pp.
22.
A. I. Breev, A. V. Shapovalov, Noncommutative reduction of the nonlinear Schrodinger equation on Lie groups, 2021 , 19 pp., https://arxiv.org/abs/2108.05180, arXiv: math-ph/2108.05180v1
23.
S. A. Siniukov, A. Yu. Trifonov, A. V. Shapovalov, “Examples of asymptotic solutions obtained by the complex germ method for the one-dimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation”, Russian Physics Journal, 64:8 (2021), 1542–1552
24.
A. V. Shapovalov, A. E. Kulagin, “Semiclassical approach to the nonlocal kinetic model of metal vapor aqctive media”, Mathematics, 9:23 (2021), 2995 , 16 pp., arXiv: math-ph/2111.05074v1
Alexander V. Shapovalov, Anton E. Kulagin, Andrey Yu. Trifonov, “The Gross–Pitaevskii equation with a nonlocal interaction in a semiclassical approximation on a curve”, Symmetry, 12:2 (2020), 201 , 25 pp. https://www.mdpi.com/2073-8994/12/2/201
A. V. Shapovalov, A. Yu. Trifonov, “Approximate solutions and symmetry of a two-component nonlocal reaction-diffusion population model of the Fisher–KPP type”, Symmetry, 11:3 (2019), 366 ;19 pp. https://www.mdpi.com/2073-8994/11/3/366/htm
A. V. Shapovalov, A. Yu. Trifonov, “Adomian decomposition method for the one-dimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation”, Russian Physics Journal, 62:4 (2019), 710–719
29.
A. V. Shapovalov, A. Yu. Trifonov, “Adomyan decomposition method for a two component nonlocal reaction-diffusion model of the Fisher–Kolmogorov–Petrovskii–Piskunov type”, Russian Physics Journal, 62:5 (2019), 835–847
30.
A. I. Breev, A. V. Shapovalov, “Vacuum quantum effects on Lie groups with bi-invariant metrics”, International Journal of Geometric Methods in Modern Physics (IJGMMP), 16:8 (2019), 1950122 , 25 pp., arXiv: 1906.01826v1 [gr-qc]
A. V. Shapovalov, A. I. Breev, “Symmetry operators and separation of variables in the (2 + 1)-dimensional Dirac equation with external electromagnetic field”, International Journal of Geometric Methods in Modern Physics, 15:5 (2018), 1850085 , 26 pp., arXiv: math-ph/1709.04644
A. V. Shapovalov, A. Yu. Trifonov, “An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher–KPP equation”, International Journal of Geometric Methods in Modern Physics, 15:6 (2018), 1850102 , 30 pp., arXiv: math.AP/1409.3158
A. V. Shapovalov, V. V. Obukhov, “Some Aspects of Nonlinearity and Self-Organization In Biosystems on Examples of Localized Excitations in the DNA Molecule and Generalized Fisher–KPP Model”, Symmetry, 10:3 (2018), 53 , 26 pp. http://www.mdpi.com/2073-8994/10/3/53/html
Yu. V. Kistenev, A. V. Borisov, M. A. Titarenko, O. D. Baydik, A. V. Shapovalov, “Diagnosis of oral lichen planus from analysis of saliva samples using terahertz time-domain spectroscopy and chemometric”, Journal of Biomedical Optics, 23:4 (2018), 045001 , 8 pp.
E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Symmetries of the One-Dimensional Fokker–Planck–Kolmogorov Equation with a Nonlocal Quadratic Nonlinearity”, Russian Physics Journal, 60:2 (2017), 284–291https://link.springer.com/article/10.1007
37.
Yu. V. Kistenev, A. V. Borisov, A. V. Shapovalov, O. D. Baydik, M. A. Titarenko, “Diagnostics of oral lichen planus based on analysis of volatile organic compounds in saliva”, Dynamics and Fluctuations in Biomedical Photonics XIV (San Francisco, California, United States | January 28, 2017), Proc. SPIE, 10063, 2017, 100630R , 7 pp. http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2608918&resultClick=1
A. I. Breev and A. V. Shapovalov, Symmetry operators and separation of variables in the (2 + 1)-dimensional Dirac equation with external electromagnetic field, 2017 , 24 pp., arXiv: arXiv:1709.04644v1
2018
39.
A. V. Shapovalov, “Approximate solutions of the one-dimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation with quasilocal competitive losses”, Russian Physics Journal, 60:9 (2018), 1461–1468
V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast III. Differentsialnoe i integralnoe ischislenie.Chast III. 3. Integralnoe ischislenie funktsii odnoi peremennoi, eds. d.f.-m.n., prof. Osetrin K.E., d.f.-m.n., prof. Bagrov V.G., Natsionalnyi issledovatelskii Tomskii politekhnicheskii universitet, Tomsk, 2017 , 494 pp.
2016
42.
A. I. Breev and A. V. Shapovalov, “The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration”, XXIII International Conference on Integrable Systems and Quantum Symmetries (ISQS-23) (Prague, 23-27 June 2015), Journal of Physics: Conference Series, 670, 2016, 012015 , 12 pp. http://iopscience.iop.org/1742-6596/670/1/012015
43.
A. V. Shapovalov, A. Yu. Trifonov, and A. L. Lisok, “Symmetry operators of the two-component Gross–Pitaevskii equation with a Manakov-type nonlocal nonlinearity”, XXIII International Conference on Integrable Systems and Quantum Symmetries (ISQS-23) (Prague, 23-27 June 2015), Journal of Physics: Conference Series, 670, 2016, 012046 , 13 pp. http://iopscience.iop.org/article/10.1088/1742-6596/670/1/012046
A. I. Breev, A. V. Shapovalov, A. V. Kozlov, “Integration the relativistic wave equations in bianchi ix cosmology model”, Computer Research and Modeling, 8:3 (2016), 433–443
45.
E. A. Levchenko , A. V. Shapovalov, A. Yu. Trifonov, “Asymptotics semiclassically concentrated on curves for the nonlocal Fisher– Kolmogorov–Petrovskii–Piskunov equation”, J. Phys. A: Math. Theor., 49 (2016), 305203 , 17 pp. http://iopscience.iop.org/article/10.1088/1751-8113/49/30/305203/meta
A. Yu. Krainov, A. V. Shapovalov, A.V., and K. M. Moiseeva, “Thermal Action of the Nanoparticle Heated by Pulse-Periodic Laser Radiation on a Biotissue”, Russian Physics Journal, 59:8 (2016), 1219-1224
2017
47.
K. A. Isakov, A. V. Shapovalov, “Quasistationary solutions of a two-component hyperbolic system on an interval”, Russian Physics Journal, 59:9 (2017), 1349–1356
48.
A. .I. Breev and A. V. Shapovalov, “Noncommutative integrability of the Klein-Gordon and Dirac equations in (2+1)-dimensional spacetime”, Russian Physics Journal, 59:11 (2017), 1956–1961http://link.springer.com/article/10.1007/s11182-017-1001-2
2016
49.
Yu. V. Kistenev, A. V. Shapovalov, D. A. Vrazhnov, V. V. Nikolaev, “Kalman filtering in the problem of noise reduction in the absorption spectra of exhaled air”, 22nd International Symposium Atmospheric and Ocean Optics: Atmospheric Physics (Tomsk, Russian Federation | June 30, 2016), Proc. SPIE, 10035, 2016, 100350A , 6 pp.
50.
Yu. V. Kistenev, A. V. Shapovalov, A. V. Borisov, A. I. Knyazkova, “Possibilities of laser spectroscopy for monitoring the profile dynamics of the volatile metabolite in exhaled air”, Proc. SPIE, 10035 (2016), 100350B , 6 pp.
2015
51.
E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Kvaziklassicheskoe priblizhenie dlya mnogomernogo nelokalnogo uravneniya Fishera–Kolmogorova–Petrovskogo–Piskunova”, Kompyuternye issledovaniya i modelirovanie, 7:2 (2015), 205 – 219http://crm.ics.org.ru/journal/issue/165/
52.
A. A. Prozorov, A. Yu. Trifonov, and A. V. Shapovalov, “Asymptotic behavior of the one-dimensional Fisher–Kolmogorov–Pertovskii–Piskunov equation with anomalous diffusion”, Russian Physics Journal, 58:3 (2015), 399–409http://link.springer.com/article/10.1007/s11182-015-0514-9
53.
A. E. Kulagin, A. Yu. Trifonov, A. V. Shapovalov, “Quasiparticles described by the Gross-Pitaevskii equation in the semiclassical approximation”, Russian Physics Journal, 58:5 (2015), 606–615 (to appear)
54.
E. A. Levchenko, A. Yu. Trifonov., A. V. Shapovalov, “Asymptotics of the multidimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation near a quasistationary solution”, Russian Physics Journal, 58:7 (2015), 952-958
55.
A. I. Breev, A. V. Shapovalov, “Polyarizatsiya vakuuma skalyarnogo polya na gruppakh Li s biinvariantnoi metrikoi”, Kompyuternye issledovaniya i modelirovanie, 7:5 (2015), 989– 999
56.
A. V. Breev, A. V. Shapovalov, The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration, 2015 , 17 pp., http://arxiv.org/abs/1509.08612, arXiv: 1509.08612 [math-ph]
57.
A. Marfin, D. V. Lychagin, A. Shapovalov, E. A. Alfiorova, “Comparison of mathematical methods of geochemical data processing”, IOP Conf. Series: Materials Science and Engineering, 91 (2015), 012083 , 7 pp.
58.
L. A. Krasnobaeva, A. V. Shapovalov, “Local conformational perturbations of the DNA molecule in the SG-model”, The 5th International Scientific Conference «New Operational Technologies» (29–30 September 2015, Tomsk, Russia), AIP Conference Proceedings, 1688, 2015, 030020 (Published online) , 6 pp. http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4936015
59.
Yu. V. Kistenev, A. V. Shapovalov, A. V. Borisov, D. A. Vrazhnov, V. V. Nikolaev, O. Yu. Nikiforova, “Wavelet based de-noising of breath air absorption spectra profiles for improved classification by principal component analysis”, The 5th International Scientific Conference «New Operational Technologies» (29–30 September 2015, Tomsk, Russia), AIP Conference Proceedings, 1688, 2015, 030010 (Published online) , 5 pp. http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4936005
D. A. Vrazhnov, A. V. Shapovalov, V. V. Nikolaev, “Solutions of nonlocal nonlinear diffusion equations in data filtering problems”, The 5th International Scientific Conference «New Operational Technologies» (29–30 September 2015, Tomsk, Russia), AIP Conference Proceedings, 1688, 2015, 030016 (Published online) , 6 pp. http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4936011
61.
A. Y. Krainov ; K. M. Moiseeva ; A. V. Shapovalov, “Thermal interaction of biological tissue with nanoparticles heated by laser radiation”, Proc. SPIE 9810, International Conference on Atomic and Molecular Pulsed Lasers XII, 981020 (December 15, 2015), Proc. International Conference on Atomic and Molecular Pulsed Lasers XII (Tomsk, Russian Federation, September 14, 2015), Proc. SPIE, 9810, eds. Victor F. Tarasenko; Andrey M. Kabanov, SPIE, 2015, 981020-1-7http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2478143&resultClick=1
Yu. V. Kistenev, A. V. Shapovalov, A. V. Borisov, D. A. Vrazhnov, V. V. Nikolaev, O. Y. Nikiforova, “Applications of principal component analysis to breath air absorption spectra profiles classification”, Proc. SPIE 9810, International Conference on Atomic and Molecular Pulsed Lasers XII, 98101Y (December 15, 2015), Proc. International Conference on Atomic and Molecular Pulsed Lasers XII (Tomsk, Russian Federation, September 14, 2015), Proc. SPIE, eds. Victor F. Tarasenko; Andrey M. Kabanov, SPIE, 2015, 98101Y-1-6http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2478141&resultClick=1
Yu. V. Kistenev, A. V. Borisov, A. V. Shapovalov, “Determination of component concentrations in models of exhaled air samples using principal component analysis and canonical correlation analysis”, Proc. SPIE 9810, XII International Conference on Atomic and Molecular Pulsed Lasers, 98101Z (December 15, 2015), Proc. International Conference on Atomic and Molecular Pulsed Lasers XII (Tomsk, Russian Federation, September 14, 2015), Proc. SPIE, 9810, eds. Victor F. Tarasenko; Andrey M. Kabanov, SPIE, 2015, 98101Z-1-6http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2478142&resultClick=1
Yu. V. Kistenev, D. A. Kuzmin, E. A. Sandykova, A. V. Shapovalov, “Quantitative comparison of the absorption spectra of the gas mixtures in analogy to the criterion of Pearson”, Proc. SPIE 9680, 21st International Symposium Atmospheric and Ocean Optics: Atmospheric Physics (Tomsk, Russian Federation, June 22, 2015), SPIE Proceedings, 96803, eds. Oleg A. Romanovskii, SPIE, 2015, 96803S-1-8http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2473089&resultClick=1
65.
Yu. V. Kistenev, A. V. Borisov, A. V. Shapovalov, “Statistical approach to the analysis of the composition of multicomponent gas mixtures using absorption laser spectroscopy”, Proc. SPIE 9680, 21st International Symposium Atmospheric and Ocean Optics: Atmospheric Physics, 968044 (November 19, 2015) (Tomsk, Russian Federation, June 22, 2015), 968044, eds. Oleg A. Romanovskii, SPIE, 2015, 968044-1-6http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2473101&resultClick=1
66.
Yu. V. Kistenev, A. V. Shapovalov, D. A. Vrazhnov, V. V. Nikolaev, O. Y. Nikiforova, “Comparison of classification methods used for analysis of complex biological gas mixtures by means of laser spectroscopy”, Proc. SPIE 9680, 21st International Symposium Atmospheric and Ocean Optics: Atmospheric Physics, 968049 (November 19, 2015) (Tomsk, Russian Federation, June 22, 2015), SPIE Proceedings, 9680, eds. Oleg A. Romanovskii, SPIE, 2015, 96804C-1-6http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2473106&resultClick=1
Yury V. Kistenev, Alexey V. Borisov, Alexander V. Shapovalov, Olga Y. Nikiforova, “Analysis of the component composition of exhaled air using laser spectroscopy and canonical correlation analysis”, Proc. SPIE 9680, 21st International Symposium Atmospheric and Ocean Optics: Atmospheric Physics, 96804C (November 19, 2015) (Tomsk, Russian Federation, June 22, 2015), SPIE Proceedings, 9680, eds. Oleg A. Romanovskii, SPIE, 2015, 96804C-1-6http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2473109&resultClick=1
E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical approximation for the nonlocal multidimensionalfisher-kolmogorov-petrovskii-piskunov equation”, Computer Research and Modeling, 7:2 (2015), 205–219
69.
A. I. Breev, A. V. Shapovalov, “Vacuum polarization of scalar field on lie groups with bi-invariantmetric”, Computer Research and Modeling, 7:5 (2015), 989–999
2014
70.
E. A. Levchenko, A. V. Shapovalov, and A. Yu. Trifonov, “Pattern formation in terms of semiclassically limited distribution on lower dimensional manifolds for the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation”, Journal of Physics A: Mathematical and Theoretical, 47 (2014), 025209 , 20 pp. http://iopscience.iop.org/1751-8121/47/2/025209/article, arXiv: arXiv:1306.3765v1
A. I. Breev, A. V. Shapovalov, Yang-Mills gauge fields conserving symmetry algebra of Dirac equation in homogeneous space, 2014 , 25 pp., http://arxiv.org/abs/1406.5033, arXiv: gr-qc/1406.5033
73.
A. V. Shapovalov, A. Yu. Trifonov, Asymptotic solutions of the 1D nonlocal Fisher–KPP equation, 2014 , 35 pp., http://arxiv.org/abs/1409.3158v1, arXiv: 1409.3158 [math.AP]
74.
A. I. Breev, A. V. Shapovalov, “Yang–Mills gauge fields conserving the symmetry algebra of the Dirac equation in a homogeneous space”, Integrable systems and quantum symmetries (ISQS-2014) (Prague, June, 23-29, 2014), Journal of Physics: Conference Series, 563, 2014, 012004 , 15 pp.
A. I. Breev, A. V. Shapovalov, “A spectrum of the Dirac operator with an external Yang-Mills gauge field on de Sitter space”, Proceedings of the International Conference “Quantum field theory and gravitation” (Tomsk, July 28-August 3 2014), Vestnik Tomskogo gosudarstvennogo pedagogicheskogo universiteta, 12(153), TGPU, Tomsk, 2014, 25-27
2013
76.
A. L. Lisok, A. V. Shapovalov, A. Yu. Trifonov, “Symmetry and Intertwining Operators for the Nonlocal Gross{Pitaevskii Equation”, SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), 9 (2013), 066 , 21 pp. http://dx.doi.org/10.3842/SIGMA.2013.066, arXiv: arXiv:1302.3326v2
E. A. Levchenko, A. V. Shapovalov, and A. Yu. Trifonov, Pattern formation in terms of semiclassically limited distribution on lower-dimensional manifolds for nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation, 2013 , 22 pp., arXiv: arXiv:1306.3765v1
78.
A. L. Lisok, A. V. Shapovalov, and A. Yu. Trifonov, Symmetry operators and intertwining operators for the nonlocal Gross–Pitaevskii equation, 2013 , 19 pp., arXiv: arXiv:1302.3326v1
2014
79.
E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Symmetry operators of the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation with a quadratic operator”, Russian Physics Journal, 56:12 (2014), 1415–1426
2013
80.
D. A. Vrazhnov, V. V. Nikolaev, A. V. Shapovalov, “Sravnitelnyi analiz metodov povysheniya ustoichivosti algoritmov slezheniya na video”, Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitelnaya tekhnika i informatika, 2013, no. 4 (25), 23-31
81.
E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Large-time asymptotic solutions of the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation”, Computer Research and Modeling, 5:4 (2013), 543–558
82.
V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast III. Differentsialnoe i integralnoe ischislenie. Chast III.1. Differentsialnoe ischislenie funktsii odnoi peremennoi, Natsionalnyi issledovatelskii Tomskii politekhnicheskii universitet, Tomsk, 2013 , 326 pp.
2012
83.
E. A. Levchenko, A. V. Shapovalov, A. Yu. Trifonov, “Symmetries of the Fisher-Kolmogorov-Petrovskii-Piskunov equation with a nonlocal nonlinearity in a semiclassical approximation”, Journal of Mathematical Analysis and Applications (JMAA), 395:2 (2012), 716-726
E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Estimate of Accuracy of Solution of the Nonlocal Fisher–Kolomogorov–Petrovskii–Piskunov Equation”, Russian Physics Journal, 55:12 (2013), 1425-1433 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 47–53, December, 2012 http://link.springer.com/journal/11182/55/12/page/1
2012
85.
D. A. Vrazhnov, A. V. Shapovalov, V. V. Nikolaev, “On quality of object tracking algorithms”, Computer Research and Modeling, 4:2 (2012), 303–313
86.
A. V. Borisov, L. A. Krasnobaeva, A. V. Shapovalov, “Influence of diffusion and convection on the chemostat dynamics”, Computer Research and Modeling, 4:1 (2012), 121–129
2011
87.
E. Zamora Sillero, A. V. Shapovlov, “Equivalent Lagrangian densities and invariant collective coordinates equations”, J. Phys. A: Math. Theor., 44:6 (2011), 065204 (11 pp)http://iopscience.iop.org/1751-8121/44/6/065204
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Evolution of initial distributions with one and two centers in a two-dimensional model of the reaction-diffusion type with a nonlocal interaction of finite radius”, Russian Physics Journal, 54:1 (2011), 32–38 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 30–35, January, 2011. http://link.springer.com/journal/11182/54/1/page/1
89.
V. A. Aleutdinova, A. V. Borisov, V. É. Shaparev, A. V. Shapovalov, “Numerical simulation of the one-dimensional population dynamics with nonlocal competitive losses and convection”, Russian Physics Journal, 54:4 (2011), 479–484 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 76–80, April, 2011
90.
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Nelokalnaya reaktsionno-diffuzionnaya dinamika formirovaniya krestoobraznykh dvumernykh dissipativnykh struktur”, Izvestiya Tomskogo politekhnicheskogo universiteta, 318:2 (2011), 48–52
91.
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Convection effect on two-dimensional dynamicsin the nonlocal reaction-diffusion model”, Computer Research and Modeling, 3:1 (2011), 55–61
92.
V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast II. .Analiticheskaya geometriya: Uchebnoe posobie, 2-e izd., ispr. i dop., eds. prof. V. G. Bagrov, prof. K. E. Osetrin, Tomskii politekhnicheskii universistet, Tomsk, 2011 , 398 pp., Dopuscheno UMO po obrazovaniyu v oblasti matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po napravleniyu podgotovki 230400 “Prikladnaya matematika” spetsialnosti 230401 “Prikladnaya matematika”
93.
V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast IV. .Ryady: Uchebnoe posobie, 2-e izd., ispr. i dop., eds. prof. V. G. Bagrov, prof. K. E. Osetrin, Tomskii politekhnicheskii universistet, Tomsk, 2011 , 344 pp., Dopuscheno UMO po obrazovaniyu v oblasti matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po napravleniyu podgotovki 230400 “Prikladnaya matematika” spetsialnosti 230401 “Prikladnaya matematika”
94.
V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast V. .Differentsialnye uravneniya: Uchebnoe posobie, 2-e izd., ispr. i dop., eds. prof. V. G. Bagrov, prof. K. E. Osetrin, Tomskii politekhnicheskii universistet, Tomsk, 2011 , Dopuscheno UMO po obrazovaniyu v oblasti matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po napravleniyu podgotovki 230400 “Prikladnaya matematika” spetsialnosti 230401 “Prikladnaya matematika”
2010
95.
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Formirovanie dissipativnoi struktury v dvumernoi populyatsionnoi dinamike s nelokalnym vzaimodeistviem”, Izvestiya Tomskogo politekhnicheskogo universiteta, 316:2 (2010), 50-53
96.
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Dvumernaya dinamika raspredelenii s odnim i dvumya tsentrami lokalizatsii v nelokalnoi reaktsionno-diffuzionnoi modeli”, Izvestiya Tomskogo politekhnicheskogo universiteta, 316:2 (2010), 54–58
97.
R. O. Rezaev, A. Yu. Trifonov, A. V. Shapovalov, “Sistema Einshteina-Erenfesta tipa (0,M) i asimptoticheskie resheniya mnogomernogo nelineinogo uravneniya Fokkera-Planka-Kolmogorova”, Kompyuternye issledovaniya i modelirovanie, 2:2 (2010), 151-160http://crm.ics.org.ru/journal/issue/121/
98.
D. A. Vrazhnov, A. V. Shapovalov, V. V. Nikolaev, “Simmetrii differentsialnykh uravnenii v zadachakh kompyuternogo zreniya”, Kompyuternye issledovaniya i modelirovanie, 2:4 (2010), 69-376http://crm.ics.org.ru/journal/issue/125/
E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Kvaziklassicheskoe priblizhenie dlya odnomernogo dvukhkomponentnogo reaktsionno-diffuzionnogo uravneniya s nelokalnoi nelineinostyu”, Vestnik Adygeiskogo gosudarstvennogo universiteta. Seriya “Estestvenno-matematicheskie i tekhnicheskie nauki”, 2010, no. 2(61), 68-79http://elibrary.ru/contents.asp?issueid=874155
100.
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Vliyanie nelineinoi diffuzii na odnomernuyu reaktsionno-diffuzionnuyu dinamiku s nelokalnym samodeistviem”, Vestnik Adygeiskogo gosudarstvennogo universiteta. Seriya “Estestvenno-matematicheskie i tekhnicheskie nauki”, 2010, no. 2(61), 89–97http://elibrary.ru/contents.asp?issueid=874155
2011
101.
A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical approximation for the twodimensional Fisher–Kolmogorov–Petrovskii– Piskunov equation with nonlocal nonlinearity in polar coordinates”, Russian Physics Journal, 53:12 (2011), 1243-1253 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 21–29, December, 2010. http://link.springer.com/journal/11182/53/12/page/1
2010
102.
D. A. Vrazhnov, A. V. Shapovalov, V. V. Nikolaev, “Symmetries of differential equations in computer vision applications”, Computer Research and Modeling, 2:4 (2010), 363–376
103.
R. O. Rezaev, A. Yu. Trifonov, A. V. Shapovalov, “The Einstein-Ehrenfest system of (0, $M$)-type and asymptotical solutions of the multidimensional nonlinear Fokker-Planck-Kolmogorov equation”, Computer Research and Modeling, 2:2 (2010), 151–160
104.
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Numerical modeling of population 2D-dynamics with nonlocal interaction”, Computer Research and Modeling, 2:1 (2010), 33–40
105.
V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast I. Lineinaya algebra: Uchebnoe posobie, 2-e izd., eds. prof. V. G. Bagrov, prof. K. E. Osetrin, Tomskii politekhnicheskii universistet, Tomsk, 2010 , 310 pp., Dopuscheno UMO po obrazovaniyu v oblasti matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po napravleniyu podgotovki 230400 “Prikladnaya matematika” spetsialnosti 230401 “Prikladnaya matematika”
106.
L. A. Krasnobaeva, A. V. Borisov, A. V. Shapovalov, Kompyuternye metody analiticheskikh vychislenii v prilozhenie k fizicheskim zadacham s ispolzovaniem matematicheskogo yazyka programmirovaniya Maple. [Elektronnyi resurs]: Laboratornyi praktikum, http://edu2.tsu.ru/eor/resourse/195/tpl/index.html, Institut distantsionnogo obrazovaniya TGU, Tomsk, 2010 , 52 pp.
2009
107.
A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, “Kvaziklassicheskie simmetrii uravneniya tipa Khartri s kvadratichnym operatorom”, Izvestiya Tomskogo politekhnicheskogo universiteta, 314:2 (2009), 66-71
108.
A. V. Borisov,R. O. Rezaev, A. Yu. Trifonov, A. V. Shapovalov, “Chislennoe modelirovanie odnomernoi populyatsionnoi dinamiki s nelokalnym vzaimodeistviem”, Izvestiya Tomskogo politekhnicheskogo universiteta, 315:2 (2009), 24–28
109.
V. A. Lyamkin, R. O. Rezaev, A. Yu. Trifonov, A. V. Shapovalov, “Sistema Einshteina-Erenfesta tipa (k, 1) dlya nelineinogo uravneniya Fokkera-Planka”, Vestnik Adygeiskogo gosudarstvennogo universiteta. Seriya “Estestvenno-matematicheskie i tekhnicheskie nauki”, 2009, no. 2(49), 26-37http://elibrary.ru/contents.asp?issueid=650571
110.
A. Yu. Trifonov, A. V. Shapovalov, “The one-dimensional Fisher–Kolmogorov equation with a nonlocal nonlinearity in a semiclassical approximation”, Russian Physics Journal, 52:9 (2009), 899-911 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 14–23, September, 2009. http://link.springer.com/article/10.1007/s11182-010-9316-2
111.
E. I. Smirnova, A. Yu. Trifonov, A. V. Shapovalov, “Formalism of semiclassical asymptotics for a two-component Hartree-type equation”, Russian Physics Journal, 52:10 (2009), 1068-1076 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 59–66, October, 2009.
112.
L. A. Krasnobaeva, A. V. Shapovalov, “Modulation of the velocity of soliton-like perturbations for the sine–Gordon equation with external force and dissipation”, Russian Physics Journal, 52:12 (2009), 1331-1338 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 75–81, December, 2009.
113.
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Kvaziklassicheskie resheniya uravneniya Grossa–Pitaevskogo, lokalizovannye v okrestnosti okruzhnosti”, Kompyuternye issledovaniya i modelirovanie, 1:4 (2009), 359-365http://crm.ics.org.ru/journal/issue/114/
114.
L. A. Krasnobaeva, A. V. Shapovalov, “Kink motion by ac external force and dissipation”, Computer Research and Modeling, 1:3 (2009), 263–271
115.
A. V. Shapovalov, A. Yu. Trifonov, E. A. Masalova, “Semiclassical asymptotics of nonlinear Fokker-Plank equation for distributions of asset returns”, Computer Research and Modeling, 1:1 (2009), 41–49
116.
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical solutions localized in a neighborhood of a circle for the Gross-Pitaevskii equation”, Computer Research and Modeling, 1:4 (2009), 359–365
117.
L. A. Krasnobaeva, A. V. Shapovalov, Solitony uravneniya sinus-Gordona, eds. d.f.-m.n. V. A. Kilin, Tomskii gosudarstvennyi universitet, Tomsk, 2009 , 192 pp., Uchebnoe posobie. Dopuscheno UMO po klassicheskomu universitetskomu obrazovaniyu v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po napravleniyu 010700 - Fizika
118.
V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. I. Lineinaya algebra: Uchebnoe posobie, eds. prof. V. G. Bagrov, prof. K. E. Osetrin, Tomskii politekhnicheskii universistet, Tomsk, 2009 , 310 pp., Dopuscheno UMO po obrazovaniyu v oblasti prikladnoi matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po spetsialnosti 073000 “Prikladnaya matematika”
2008
119.
L. A. Krasnobaeva, A. V. Shapovalov, “Kink Velosity in Nonstationary External Fields for the Sine -Gordon Model with Allowance for Dissipation Effects”, Russian Physics Journal, 51:1 (2008), 89-98 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 77–84, January, 2008 http://link.springer.com/article/10.1007/s11182-008-9020-7
120.
L. A. Krasnobaeva, A. V. Shapovalov, “Kink dynamics in the medium with a random force and dissipation in the sine-Gordon model”, Russian Physics Journal, 51:2 (2008), 158-167 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 44–51, February, 2008. http://link.springer.com/article/10.1007/s11182-008-9040-3
121.
A. V. Shapovalov, A. Yu. Trifonov, E. A. Masalova, “Kvaziklassicheskoe priblizhenie dlya nelineninogo uravneniya Fokkera - Planka s kvadratichnoi diffuziei v modelyakh dokhodnostei aktivov”, “Matematika. Kompyuter. Obrazovanie”. Cbornik trudov XV mezhdunarodnoi konferentsii, Izhevsk: Nauchno-izdatelskii tsentr “Regulyarnaya i khaoticheskaya dinamika” (Moskovskaya oblast., g. Puschino, 8 yanvarya—2 fevralya 2008 goda), 1, eds. Pod obschei redaktsiei G.Yu. Riznichenko, Nauchno-izdatelskii tsentr “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2008, 181-189http://www.mce.biophys.msu.ru/rus/archive/proceedings/mce15/part22253/doc21830/
122.
A. V. Shapovalov, A. Yu. Trifonov, E. A. Masalova, “Nonlinear Fokker–Planck Equation in the Model of Asset Returns”, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 4 (2008), 038 , 10 pp. http://www.emis.de/journals/SIGMA/2008/
A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, “Quasi-energy spectral series for a nonlocal Gross-Pitaevskii equation”, Russian Physics Journal, 50:7 (2007), 695-709 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 58–69, July, 2007. http://link.springer.com/article/10.1007/s11182-007-0104-6
124.
F. N. Litvinets, A. V. Shapovalov, A. Yu. Trifonov, “Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field”, Journal of Physics A: Mathematical and Theoretical, 40:36 (2007), 11129-11149http://adsabs.harvard.edu/abs/2007JPhA...4011129L, arXiv: arXiv:math-ph/0610076
125.
Elias Zamora-Sillero and A. V. Shapovalov, “Soliton fractals in Korteweg de Vries equation”, Physical Review, E., 76:4 (2007), 046612-1 — 046612-10 , URL: http://link.aps.org/doi/10.1103/PhysRevE.76.04661 http://pre.aps.org/abstract/PRE/v76/i4/e046612
Elias Zamora-Sillero, A. V. Shapovalov, and Francisco J. Esteban., “Formation, control and dynamics of $\displaystyle N$ localized structures in the Peyrard-Bishop model”, Physical Review, E., 76:6 (2007), 066603-1 — 066603-13 , URL:http://link.aps.org/doi/10.1103/PhysRevE.76.066603 http://pre.aps.org/abstract/PRE/v76/i6/e066603
A. L. Lisok, A. Yu. Trifonov, and A. V. Shapovalov, Semiclassical symmetry of the Gross-Pitaevskii equation with quadratic nonlocal Hamiltonian, 2007 , 8 pp., arXiv: math-ph/0711.1658
128.
A. V. Shapovalov, A. Yu. Trifonov, E. A. Masalova, “Raspredelenie dokhodnostei finansovykh aktivov i nelineinoe uravnenie Fokkera-Planka-Kolmogorova”, Matematika. Kompyuter. Obrazovanie: Sb. nauchnykh trudov., Trudy Chetyrnadtsatoi Mezhdunarodnoi Konferentsii MATEMATIKA. KOMPYuTER. OBRAZOVANIE (g. Puschino, 22 - 27 yanvarya 2007g.), 1, eds. G. Yu. Riznichenko i A. B. Rubin, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva-Izhevsk, 2007, 186-193http://www.mce.su/rus/MCE-2007/
129.
N. A. Matyushenkova, A. V. Shapovalov, “Dinamicheskaya model vliyaniya reitinga na raspredelenie finansirovaniya podrazdeleniya vuza v usloviyakh konkurentsii”, Matematika. Kompyuter. Obrazovanie: Sb. nauchnykh trudov, Trudy Chetyrnadtsatoi Mezhdunarodnoi Konferentsii MATEMATIKA. KOMPYuTER. OBRAZOVANIE (g. Puschino, 22 - 27 yanvarya 2007 g.), 1, eds. G. Yu. Riznichenko i A. B. Rubin, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva-Izhevsk, 2007, 230-238http://www.mce.su/rus/MCE-2007/
130.
Alexander V. Shapovalov, Roman O. Rezaev, Andrey Yu. Trifonov, “Symmetry Operators for the Fokker–Plank–Kolmogorov Equation with Nonlocal Quadratic Nonlinearity”, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 3:Paper 005 (2007), 005-1–16 (16 pp.)http://www.emis.de/journals/SIGMA/2007/
V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast V. Differentsialnye uravneniya: uchebnoe posobie, eds. prof. V. G. Bagrov, prof. K. E. Osetrin, Tomskii politekhnicheskii universistet, Tomsk, 2007 , 396 pp., Dopuscheno UMO po obrazovaniyu v oblasti prikladnoi matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po spetsialnosti 073000 “Prikladnaya matematika”
2006
132.
F. N. Litvinets, A. V. Shapovalov, A. Yu. Trifonov, “Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential”, Journal of Physics A: Mathematical and General, 39 (2006), 1191-1206 , arXiv: math-ph/0510054
F. N. Litvinets, A. Yu. Trifonov, A. V. Shapovalov, Berry phases for 3D Hartree type equations with a quadratic potential and a uniform magnetic field, 2006 , 15 pp., http://arxiv.org/abs/math-ph/0610076, arXiv: math-ph/0610076
134.
A. L. Lisok, A. Yu. Trifonov, and A. V. Shapovalov, Quasi-energy spectral series and the Aharonov-Anandan phase for the nonlocal Gross–Pitaevsky equation, 2006 , 17 pp., http://arxiv.org/abs/math-ph/0612017, arXiv: math-ph/0612017
135.
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “A semiclassical approximation for the nonstationary two-dimensional nonlinear Schrödinger equation with an external field in polar coordinates”, Russian Physics Journal, 49:7 (2006), 734-743 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp.49-56, July, 2006. http://link.springer.com/article/10.1007/s11182-006-0169-7
136.
D. N. Zhabin, E. A. Masalova, A. V. Shapovalov, “Dinamicheskoe upravlenie investitsionnym portfelem”, Vestnik Tomskogo gosudarstvennogo universiteta, 2006, no. 290, 158-162http://elibrary.ru/item.asp?id=12157968
137.
S. I. Karas, Yu. I. Kistenev, O. Yu. Nikiforova, Ya. S. Pekker, V. A. Fokin, A. V. Shapovalov, Nelineinyi analiz mediko-biologicheskikh dannykh, Tomskii politekhnicheskii universitet, Tomsk, 2006 , 118 pp.
138.
N. A. Matyushenkova, A. V. Shapovalov, “Issledovanie vliyaniya ob'ema finansirovaniya podrazdeleniya vuza na ego reiting”, “Matematika. Kompyuter. Obrazovanie”. Cb. trudov XIII mezhdunarodnoi konferentsii (Dubna, 23 - 28 yanvarya), 1, eds. G.Yu.Riznichenko, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva-Izhevsk, 2006, 326-333http://www.mce.su/rus/archive/proceedings/mce13/sect1032/
139.
A. V. Shapovalov, A. Yu. Trifonov, E. A. Masalova, “Dinamika tseny optsiona dlya aktivov, opisyvaemykh Blend- raspredeleniem”, “Matematika. Kompyuter. Obrazovanie”. Cb. trudov XIII mezhdunarodnoi konferentsii (Dubna, 23 - 28 yanvarya), 1, eds. G. Yu. Riznichenko, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva-Izhevsk, 2006, 338-346http://www.mce.su/rus/archive/proceedings/mce13/sect1032/
140.
L. V. Yakushevich, L. A. Krasnobaeva, A. V. Shapovalov, N. R. Kvintero, “Raznoobrazie nelineinykh volnovykh reshenii v sinus- Gordon modeli DNK”, “Matematika. Kompyuter. Obrazovanie”. Cb. trudov XIII mezhdunarodnoi konferentsii (Dubna, 23 - 28 yanvarya), 2, eds. G.Yu.Riznichenko, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva-Izhevsk, 2006, 383-391http://www.mce.su/rus/archive/proceedings/mce13/sect284/
141.
V. N. Zadorozhnyi, V. F. Zalmezh, A. Yu. Trifonov, A. V. Shapovalov, Vysshaya matematika dlya tekhnicheskikh universitetov. Chast IV. .Ryady: Uchebnoe posobie, eds. prof. V. G. Bagrov, prof. I. L. Bukhbinder, Tomskii politekhnicheskii universistet, Tomsk, 2006 , 343 pp., Dopuscheno UMO po obrazovaniyu v oblasti prikladnoi matematiki i upravleniya kachestvom v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po spetsialnosti 073000 “Prikladnaya matematika”
2005
142.
Alexey Borisov, Alexander Shapovalov, Andrey Trifonov, “Transverse Evolution Operator for the Gross–Pitaevskii Equation in Semiclassical Approximation”, SIGMA, 1:019 (2005), 17 pp.
Alexander Shapovalov, Andrey Trifonov, Alexander Lisok, “Exact Solutions and Symmetry Operators for the Nonlocal Gross–Pitaevskii Equation with Quadratic Potential”, SIGMA, 1:007 (2005), 14 pp.
A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, “Symmetry operators of a Hartree-type equation with quadratic potential”, Siberian Math. J., 46:1 (2005), 119–132
145.
A. Yu. Trifonov, A. V. Bezverbny, A. V. Borisov, A. V. Shapovalov, “Temporal kinetics of atomic ensemble in a light field”, Proc. Fourth Int. Symposium «Modern Problems of Laser Physics» (MPLP 2004), Novosibirsk. — 2005. — R. 323–330. (August 22-27, 2004, Novosibirsk), ISBN 5-85957-044-9, eds. Sergei N. Bagayev, Pavel V. Pokasov, Institute of Laser Physics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, 2005, 65-76
146.
L. V. Yakushevich, L. A. Krasnobaeva, A. V. Shapovalov, N. R. Quintero, “One- and two- soliton solutions of the sine-Gordon equation as applied to DNA”, Byophysics, 50:3 (2005), 404-409http://elibrary.ru/item.asp?id=13496208
147.
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “The Nonlinear Schrodinger Equation for a Many-Dimensional System in an Oscillator Field”, Russian Physics Journal, 48:7 (2005), 746-753http://link.springer.com/article/10.1007/s11182-005-0196-9
148.
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Kvaziklassicheskoe priblizhenie dlya mnogomernogo nelineninogo uravneniya Shredingera s vneshnim polem”, “Matematika. Kompyuter. Obrazovanie”. Cb. trudov XII mezhdunarodnoi konferentsii., 2, eds. G. Yu. Riznichenko, Izhevsk: Nauchno-izdatelskii tsentr “Regulyarnaya i khaoticheskaya dinamika”, Moskva-Izhevsk, 2005, 648-659http://www.mce.su/rus/archive/proceedings/mce12/sect283/
2004
149.
A. V. Bezverbny, A. V. Shapovalov, “Modelling of kinetics of atomic ensemble in a light field using the langevin equation”, Matem. Mod., 16:9 (2004), 49–60
150.
A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, “Green's Function of a Hartree-Type Equation with a Quadratic Potential”, Theoret. and Math. Phys., 141:2 (2004), 1528–1541
151.
A. V. Shapovalov, A. Yu. Trifonov, and A. L. Lisok, “Semiclassical approach to the geometric phase theory for the Hartree type equation”, The Proceedings of Fifth International Conference “Symmetry in Nonlinear Mathematical Physics”, Part 3, Proceedings of Institute of Mathematics of NAS of Ukraine, 50, eds. Editors: A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A.Yehorchenko,, Institute of Mathematics, 2004, Kyiv, 2004, 1454-1465http://www.imath.kiev.ua/~snmp2003/Proceedings/part3.html
152.
A. L. Lisok, A. Yu. Trifonov, and A. V. Sapovalov, “The evolution operator of the Hartree-type equation with a quadratic potential”, Journal of Physics A: Mathematical and General, 37 (2004), 4535-4556http://iopscience.iop.org/0305-4470/37/16
A. V. Borisov, Yu. V. Kistenev, A. Yu. Trifonov, A. V. Shapovalov, “Investigation of the Dynamics of a Soliton-Like Solution to the Nonlinear Schrödinger Equation with an External Field”, Russian Physics Journal, 47:1 (2004), 25-30http://link.springer.com/article/10.1023/B
154.
A. L. Lisok, F. N. Litvinets, A. Yu. Trifonov, A. V. Shapovalov, “The Geometric Phases and Quasienergy Spectral Series of a Hartree-Type Equation with a Quadratic Potential”, Russian Physics Journal, 47:4 (2004), 405-413http://link.springer.com/article/10.1023/B
155.
A. V. Bezverbnyi, A. V. Shapovalov, “Stokhasticheskaya dinamika atomov v rezonansnom svetovom pole v kvaziklassicheskom priblizhenii”, Optika i spektroskopiya, 97:1 (2004), 80-87
156.
V. G. Bagrov, A. V. Shapovalov, “Klassicheskoe razdelenie peremennykh v lineinom differentsialnom uravnenii vtorogo poryadka neparabolicheskogo tipa”, Trudy XV Mezhdunarodnoi letnei shkoly-seminara “Volga” po sovremennym problemam teoreticheskoi i matematicheskoi fiziki. Petrovskie chteniya, 324 str., Noveishie problemy teorii polya, 4, eds. A. V. Aminova, Kheter, Kazan, 2004, 25-60
157.
A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, “Kvaziklassicheskoe priblizhenie v teorii geometricheskikh faz dlya uravneniya tipa Khartri”, Trudy XV Mezhdunarodnoi letnei shkoly-seminara “Volga” po sovremennym problemam teoreticheskoi i matematicheskoi fiziki. Petrovskie chteniya, 324 str., Noveishie problemy teorii polya, 4, eds. A.V. Aminova, Kheter, Kazan, 2004, 191-202
158.
F. N. Litvinets, A. Yu. Trifonov, A. V. Shapovalov, “Faza Aaronova-Anandana uravneniya tipa Khartri s kvadratichnym potentsialom”, Trudy XV Mezhdunarodnoi letnei shkoly-seminara “Volga” po sovremennym problemam teoreticheskoi i matematicheskoi fiziki. Petrovskie chteniya, 324 str., Noveishie problemy teorii polya, 4, eds. A. V. Aminova, Kheter, Kazan, 2004, 203-216
2003
159.
M. D. Noskov, V. V. Lopatin, A. A. Cheglokov, A. V. Shapovalov, “Investigation of Discharge Channel Elongation under Thermal Dielectric Breakdown”, Russian Physics Journal, 46:1 (2003), 91-95http://link.springer.com/article/10.1023/A
160.
E. V. Evdokimov , K. E. Evdokimov, and A. V. Shapovalov, “Peculiarities of Resonance Chaos Suppression in Populations with Non-overlapping Generations”, Physica D: Nonlinear Phenomena, 179:1-2 (2003), 115-127http://www.sciencedirect.com/science/article/pii/S0167278903000095
E. V. Evdokimov, A. V. Shapovalov, “Geometricheskie metody v populyatsionnoi dinamike”, Lektsionnye zametki po teoreticheskoi i matematicheskoi fizike, 12 Mezhdunarodnaya letnyaya shkola-seminar po sovremennym problemam teoreticheskoi i matematicheskoi fizike “Volga -12” (Petrovskiei chteniya) (Kazan, 22 iyunya-2 iyulya 2000 g.), “Volga -12” (Petrovskiei chteniya), 3. Ch.2, eds. A. V. Aminova, KGU, Kazan, 2003, 138-156
162.
A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov, D. E. Yakovlev, “Kvaziklassicheskie spektralnye serii i geometricheskie fazy dlya uravneniya tipa Khartri”, “Noveishie problemy teorii polya 2001-2002”, Trudy XIII-XIV Mezhdunarodnoi letnei shkoly-seminara po sovremennym problemam teoreticheskoi i matematicheskoi fiziki “Volga 13'01-14-02” (Petrovskie chteniya), eds. A. V. Aminova, KGU, Kazan, 2003, 264-279
163.
G. N. Serezhnikov, A. Yu. Trifonov, A. V. Shapovalov, “Superpozitsiya uedinennykh voln dlya uravneniya tipa Khartri s gaussovym potentsialom”, “Noveishie problemy teorii polya 2001-2002”, Trudy XIII-XIV Mezhdunarodnoi letnei shkoly-seminara po sovremennym problemam teoreticheskoi i matematicheskoi fiziki “Volga 13'01-14-02” (Petrovskie chteniya), eds. A. V. Aminova, KGU, Kazan, 2003, 387-395
164.
A. Yu Trifonov, A. V. Shapovalov, D. E. Yakovlev, “Kvaziklassicheski sosredotochennye resheniya odnomernogo uravneniya Fokkera-Planka- Kolmogorova”, “Noveishie problemy teorii polya 2001-2002”, Trudy XIII-XIV Mezhdunarodnoi letnei shkoly-seminara po sovremennym problemam teoreticheskoi i matematicheskoi fiziki “Volga 13'01-14-02” (Petrovskie chteniya), eds. A. V. Aminova, KGU, Kazan, 2003, 442-452
165.
A. V. Borisov, Yu. V. Kistenev, A. Yu. Trifonov, A. V. Shapovalov, “Kompyutnrnoe modelirovanie asimptoticheskogo NUSh - solitona vo vneshnikh polyakh spetsialnogo vida”, Sb. Trudov 10 Mezhdunarodnoi konferentsii "Matematika. Kompyuter. Obrazovanie." (g. Puschino, 20-25 yanvarya 2003 g.), 2, eds. G. Yu. Riznichenko, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva-Izhevsk, 2003, 176 - 183http://www.mce.su/rus/archive/proceedings/mce10/part15632/
2002
166.
V. V. Belov, A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical Trajectory-Coherent Approximations of Hartree-Type Equations”, Theoret. and Math. Phys., 130:3 (2002), 391–418
167.
A. V. Shapovalov, A. Yu. Trifonov, “Semiclassically consentrated waves for the generalized nonlinear Shrodinger equation with external field”, Proceedings of IV Int. Conference “Symmetry in Nonlinear Mathematical Physics”, Proc. Institute of Mathematics of NAN of Ukraine, Part 2 (Kyiv, Ukraine, 9-15 July, 2001), 32, eds. A. G. Nikitin, V. M. Boiko, and R. O. Popovich, NAN of Ukraine, Institute of Mathematics, Kyiv, 2002, 701-711
168.
A. Yu. Trifonov, A. V. Shapovalov, “Geometricheskaya faza dlya uravneniya tipa Khartri v kvaziklassicheskom traektorno-kogerentnom priblizhenii”, Trudy III Mezhdunarodnoi konferentsii “Simmetriya i differentsialnye uravneniya” (Krasnoyarsk, Rossiya, 25-29 avgusta 2002 g.), eds. V. K. Andreeva, In-t vychislitelnogo modelirovaniya SO RAN.- Krasnoyarsk, Krasnoyarsk, 2002, 220-225
169.
V. V. Belov, A. Yu. Trifonov, A. V. Shapovalov, “The Trajectory-Coherent Approximation and the System of Moments for the Hartree Type Equation”, International Journal of Mathematics and Mathematical Science, 32:6 (2002), 325-370http://www.hindawi.com/journals/ijmms/2002/931236/abs/
A. Yu. Trifonov, A. V. Shapovalov, “Uravnenie Fokkera-Planka_Kolmogorova v kvaziklassicheskom priblizhenii”, Sbornik Trudov 9-oi Mezhdunarodnoi Konferentsii “Matematika. Kompyuter. Obrazovanie” (v 2-kh tomakh) (Dubna, 28.01-02.02.2002 g), 2, eds. G. Yu. Riznichenko, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva, Izhevsk, 2002, 356-367
171.
A. V. Borisov, A. Yu. Kistenev, A. Yu. Trifonov, A. V. Shapovalov, “Opticheskii solitonopodobnyi puchok v kubichno-nelineinoi poperechno-neodnorodnoi srede”, Trudy Mezhdunarodnogo opticheskogo kongressa “Optika XXI vek. Fundamentalnye problemy optiki-2002” (Sankt-Peterburg, 14-17 oktyabrya 2002), SPbGITMO (TU), Sankt-Peterburg, 2002, 22-24
2001
172.
M. D. Noskov, A. A. Cheglokov, A. V. Shapovalov, “Dynamics of the Thermal Instability Evolution in Dielectric Breakdown”, Russian Physics Journal, 44:1 (2001), 48-54http://link.springer.com/article/10.1023/A
173.
A. Cheglokov, M. Noskov, V. Lopatin, A. Shapovalov, “Simulation of sparkchannel formation for electrical discharge technology”, Proc.of the 5-th Korea-Russia Int. Symp. on Sciemnce and Technology, KORUS 2001 (Tomsk, Russia, June 26-July 8), 1, Tomsk Polytechnic University, Tomsk, 2001, 224-228
174.
M. D. Noskov, V. V. Lopatin, A. A. Cheglokov, A. V. Shapovalov, “Computer simulation of discharge channel propagation in solid dielectric”, ICSD'01. Proceedings of the 20001 IEEE 7th International Conference on Solid Dielectrics (Cat. No.01CH37117) (Eindhoven, the Netherlands, June 25-29, 2001), Eindhoven, Eindhoven, the Netherlands, 2001, 465-468http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=7584
A. V. Borisov, A. Yu. Trifonov, A. V. Shapovalov, “Odnomernyi NUSh-soliton vo vneshnem pole. Poluklassichenskii podkhod i kompyuternoe modelirovanieyu”, Trudy mezhdunarodnoi konferentsii “Matematicheskie modeli i metody ikh issledovaniya” v 2-kh tomakh (Krasnoyarsk, Rossiya, 16-21 avgusta 2000 g.), 2, eds. V. K. Andreeva, Yu. V. Shtanko, In-t vychislitelnogo modelirovaniya SO RAN, Krasnoyarsk, 2001, 111 - 115
176.
V. V. Lopatin, M. D. Noskov, A. A. Cheglokov, A. V. Shapovalov, “Modelirovanie razvitiya razryadnogo kanala v tverdykh dielektrikakh”, Trudy mezhdunarodnoi konferentsii “Matematicheskie modeli i metody ikh issledovaniya” v 2-kh tomakh (Krasnoyarsk, Rossiya, 16-21 avgusta 2000 g.), 2, eds. V. K. Andreeva, Yu. V. Shtanko, In-t vychislitelnogo modelirovaniya SO RAN, Krasnoyarsk, 2001, 69-73
177.
A. Yu. Trifonov, A. V. Shapovalov, “Vozmuschenie poluklassicheskoi vektornoi uedinennoi volny”, Trudy mezhdunarodnoi konferentsii “Matematicheskie modeli i metody ikh issledovaniya” v 2-kh tomakh (Krasnoyarsk, Rossiya, 16-21 avgusta 2000 g.), 2, eds. V. K. Andreeva, Yu. V. Shtanko, In-t vychislitelnogo modelirovaniya SO RAN, Krasnoyarsk, 2001, 214-219
178.
A. Yu. Trifonov, A. V. Shapovalov, D. E. Yakovlev, “Odnomernoe uravnenie Fokkera-Planka -Kolmogorova v kvaziklassicheskom traektorno-kogerentnom priblizhenii”, Trudy mezhdunarodnoi konferentsii “Matematicheskie modeli i metody ikh issledovaniya” v 2-kh tomakh (Krasnoyarsk, Rossiya, 16-21 avgusta 2000 g.), 2, eds. V. K. Andreeva, Yu. V. Shtanko, In-t vychislitelnogo modelirovaniya SO RAN, 2001, 219-226
179.
A. Yu. Trifonov, A. V. Shapovalov, S. A. Shirokov, “Asimptoticheskaya vektornaya uedinennaya volna vo vneshnem pole”, Trudy “IV Mezhdunarodnoi konferentsii po matematicheskomu modelirovaniyu” v 2-kh tomakh (Moskva, 27 iyunya- 1 iyulya 2000 g.), 2, STANKIN, Moskva, 2001, 176-183
180.
A. Yu. Trifonov, A. V. Shapovalov, S. A. Shirokov, “Odnosolitonnoe VKB-reshenie vektornogo nelineinogo uravneniya Shredingera s vneshnim polem”, Trudy "VIII Mezhdunarodnoi konferentsii Matematika, Kompyuter, Obrazovanie." (g. Puschino, Moskovskoi obl., 31 yanvarya - 4 fevralya 2000 g.), Vyp. 8, eds. G. Yu. Riznichenko, Progress-Traditsiya, Moskva, 2001, 311-316
181.
E .V. Evdokimov, A. V. Shapovalov, “Proizvodstvo informatsii v khode mikroevolyutsii protochnykh gaploidnykh populyatsii. Variatsionnyi podkhod na osnove formalizma Dzheinsa.”, Trudy mezhdunarodnoi konferentsii, posvyaschennoi 90-letiyu so dnya rozhdeniya A.A. Lyapunova. (Novosibirsk, Akademgorodok, 8-11 oktyabrya 2001 g.), Novosibirsk, SO RAN, Novosibirsk, 2001, 10 s.http://www.sbras.ru/ws/Lyap2001/
182.
A. V. Shapovalov, E. V. Evdokimov, “Determinirovannyi khaos i ego reduktsiya v mikroevolyutsionnoi modeli Rikkera-Meya”, Trudy mezhdunarodnoi konferentsii, posvyaschennoi 90-letiyu so dnya rozhdeniya A.A. Lyapunova. (Novosibirsk, Akademgorodok, 8-11 oktyabrya 2001 g.), Novosibirsk, SO RAN, Novosibirsk, 2001, 5 s.http://www.sbras.ru/ws/Lyap2001/
183.
E. V. Evdokimov, A. V. Shapovalov, “Determinirovannyi khaos v dinamike populyatsii kak evolyutsionnyi faktor”, Evolyutsionnaya biologiya: Materialy konferentsii “Problema vida i vidoobrazovaniya”, 1, eds. V.N.Stegnii, Tomskii gosudarstvennyi universitet, Tomsk, 2001, 245-263
2000
184.
Ya. V. Lisitsyn, A. V. Shapovalov, “Integrable $N$-dimensional systems on the Hopf algebra and $q$-deformations”, Theoret. and Math. Phys., 124:3 (2000), 1172–1186
185.
V.D. Baranov, V.V. Belov, A.Yu. Trifonov, A.V. Shapovalov, “Kvaziklassicheskoe traektorno-kogerentnoe priblizhenie dlya uravneniya tipa Khartri”, “Noveishie problemy teorii polya. 1999-2000”., eds. A.V. Aminova, Kazanskii gosudarstvennyi universistet, Kazan, 2000, 22-43
186.
L. V. Gritsenko, I. P. Susak, A. Yu. Trifonov, A. V. Shapovalov, “Kvaziklassicheskie resheniya dvukhkomponentnogo uravneniya Shredingera”, “Noveishie problemy teorii polya. 1999-2000”., eds. A.V. Aminova, Kazanskii gosudarstvennyi universistet, Kazan, 2000, 75-84
187.
Ya.V. Lisitsyn, A.V. Shapovalov, “Gamiltoniany $N$- mernykh integrirkemykh sistem na algebre Khopfa i $q$-deformatsiya”, “Noveishie problemy teorii polya. 1999-2000”., eds. A.V. Aminova, Kazanskii gosudarstvennyi universistet, Kazan, 2000, 204-214
188.
E. V. Evdokimov, A. V. Shapovalov, “Janes approach to the dynamics of Darwin systems”, Russian Physics Journal, 43:6 (2000), 488-492 , Translated from Izvestiya Vysshikh, Uchebnykh Zavedenii, Fizika, No. 6, pp. 52–57, June, 2000. http://link.springer.com/article/10.1007/BF02508629
189.
E. V. Evdokimov, M. P. Pecherkin, A. V. Shapovalov, “Hamiltonian approach to the dynamics of a chemostat”, Russian Physics Journal, 43:7 (2000), 568-575 , Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–53, July, 2000.
190.
V. V. Belov, G. N. Serezhnikov, A. Yu. Trifonov, A. V. Shapovalov, “Sistema Gamiltona-Erenfesta i uravneniya tipa Khartri”, Trudy mezhdunarodnoi konferentsii “Simmetriya i differentsialnye uravneniya”. (Krasnoyarsk, Rossiya, 21-25 avgusta 2000 g.), eds. V.K. Andreeva i Yu.V. Shtanko, In-t vychislitelnogo modelirovaniya SO RAN, 375 s., Krasnoyarsk, 2000, 39-42
191.
A. Yu. Trifonov, A. V. Shapovalov, “Poluklassicheskie uedinennye volny vektornogo nelineinogo uravneniya Shredingera.”, Trudy mezhdunarodnoi konferentsii “Simmetriya i differentsialnye uravneniya”. (Krasnoyarsk, Rossiya, 21-25 avgusta 2000 g.), eds. V.K. Andreeva i Yu.V. Shtanko, In-t vychislitelnogo modelirovaniya SO RAN, 375 s., Krasnoyarsk, 2000, 226-229
192.
M. Noskov, A. Cheglokov, A. Shapovalov, “Computer investigation of spatial-temporal evolution of the thermal instability”, Proc. of 2000 IEEE Conf on Electrical Insulation and Dielectric Phenomena. (Victoria, British Columbia, Canada, October, 15-18), University of Victoria, Victoria, 2000, 453-456
193.
V. V. Belov, A. Yu. Trifonov, A. V. Shapovalov, The Trajectory-Coherent Approximation and the System of Moments for the Hartree Type Equation, 2000 , 35 pp., http://arxiv.org/abs/math-ph/0012046, arXiv: arXiv:math-ph/0012046
Yu. V. Kistenev and A. V. Shapovalov, “Solitary Waves in Two-Component Resonantly Absorbing Media.”, Mathematical Models of Non-Linear Exitations, Transfer, Dynamics, and Control in Condenced Systems and Other Media, eds. L.A. Uvarova, Plenum Publishing Corporation, Ney York, USA, 1999, 85-92
196.
V. M. Komarov, A. V. Kabanov, Yu. A. Lazarev, A. V. Shapovalov, “Kompyuternoe modelirovanie skrytogo polimorfizma vodorodnogo svyazyvaniya azotistykh osnovanii v strukture kanonicheskikh i khugstenovskikh par”, Trudy VI Mezhdunarodnoi konferentsii “Matematika, kompyuter, obrazovanie”, eds. G.Yu. Riznichenko, Progress-traditsi, Moskva, 1999, 1-5
197.
Yu. V. Kistenev, A. V. Shapovalov, “Spontannoe solitonoobrazovanie v rezonansno pogloschayuschei dvukhkomponentnoi srede”, Optika i spektroskopiya, 87:3 (1999), 433-438
198.
Yu. V. Kistenev, Yu. N. Ponomarev, A. V. Shapovalov, “Formirovanie solitonopodobnykh impulsov v rezonansnoi usilivayusche-pogloschayuschei srede”, Kvantovaya elektronika, 29:1 (1999), 1-5
O. V. Zhdaneev, G. N. Serezhnikov, A. Yu. Trifonov, A. V. Shapovalov, “Semiclassical trajectory-coherent states of the nonlinear Schrödinger equation with unitary nonlinearity”, Russian Physics Journal, 42:7 (1999), 598-606 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 15–23, July, 1999. http://link.springer.com/article/10.1007/BF02513223
200.
Yu. V. Kistenev, Yu. V. Ponomarev, A. V. Shapovalov, “Fraktalnye svoistva spektrov pogloscheniya gazovykh komponent atmosfery”, Optika atmosfery i okeana, 12:9 (1999), 835-839
201.
Yu. V. Kistenev, Yu. N. Ponomarev, A. V. Shapovalov, “Soliton formation in a resonant amplifying—absorbing medium”, Quantrum Electron., 29:10 (1999), 894–898
A. V. Shapovalov, E. V. Evdokimov, The geometry of the Fisher selection dynamics, 1998 , 9 pp., arXiv: physics/9805006
204.
Yu. V. Kistenev, A. V. Shapovalov, “Spontaneous soliton formation in two-component resonantly absorbing media”, Proc. SPIE, 3485 (1998), 450-454
205.
O. V. Zhdaneev, G. N. Serezhnikov, A. Yu. Trifonov, A. V. Shapovalov, “Uravneniya Shredingera s unitarnoi nelineinostyu v kvaziklassicheskom traektorno-kogerentnom priblizhenii”, ISBN 5-89423-081-0, “Noveishie problemy teorii polya. 1998": tr. Mezhdunar. letnei shk.-seminara ‘`Volga-10’98” po sovremen. probl. teoret. i mat. fiziki (Kazan,), eds. A. V. Aminova, Kazanskii gosudarstvennyi universitet, Kazan, 1998, 76-83
206.
E. V. Evdokimov, A. V. Shapovalov, “Determinirovannyi khaos kak faktor biologicheskoi evolyutsii”, Filosofiya Nauki, 1998, no. 1(4), 42-53
207.
Ya. V. Lisitsyn, A. V. Shapovalov, “Reduction of quantum analogs of Hamiltonian systems described by Lie algebras to orbits in a coadjoint representation”, Russian Physics Journal, 41:5 (1998), 460-464 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 69–74, May, 1998. http://link.springer.com/article/10.1007/BF02766506
1997
208.
A. V. Shapovalov, E. V. Evdokimov, Hamiltonian Dynamics of Darwin Systems, 1997 , 22 pp., arXiv: physics/9701012
209.
A. V. Shapovalov, E. V. Evdokimov, K. E. Evdokimov, Yu. A. Kreidun, “Kvazirezonansnye svoistva periodicheski vozmuschennykh odnoparametricheskikh logisticheski-podobnykh otobrazhenii”, Zhurnal fizicheskoi khimii, 71:11 (1997), 1999–2004
210.
E. V. Evdokimov, A. V. Shapovalov, “Hamiltonian approach to the dynamics of Darwinian systems”, Russian Physics Journal, 40:7 (1997), 610-615 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 23–28, July, 1997., arXiv: physics/9701012
211.
A. V. Shapovalov, Yu. V. Kistenev, “Opticheskie kharakteristiki rezonansno pogloschayuschego multifraktala Bezikovicha”, Trudy Mezhdunar. nauch. konf. “Matem. modeli nelin. vozbuzhdenii, perenosa, dinamiki, upravleniya v kondensir. sistemakh i dr. sredakh” (Tver, 2-5 iyulya 1996 g.), Tverskoi gosudarstvennyi politekhnicheskii universitet, Tver, 1997, 98-106
212.
Yu. V. Kistenev, A. V. Shapovalov, “Spontaneous soliton formation in a region of vibration-rotation transition of molecular multi-component media”, Proc. SPIE, 3090 (1997), 125-128
213.
Ya. V Lisytsin., A. V. Shapovalov, Separation of variables via integral transformations, 1997 , 14 pp., arXiv: solv-int/9709001
1996
214.
A. A. Drokin, A. V. Shapovalov, I. V. Shirokov, “Local symmetry algebra of Shrödinger equation for Hydrogen atom”, Theoret. and Math. Phys., 106:2 (1996), 227–236
215.
A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration method for linear partial differential equations. Functional algebras and dimensional reduction”, Theoret. and Math. Phys., 106:1 (1996), 1–10
216.
Yu. V. Kistenev, A. V. Shapovalov, “Spectral distortions of optical pulses in resonant media of complex spatial structure”, Russian Physics Journal, 39:5 (1996), 435-441 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 47–54, May, 1996.
217.
A. V. Kistenev, A. V. Shapovalov, “Absorbtsionnye svoistva rezonansnykh multifraktalnykh sred”, Optika i spektroskopiya, 80:4 (1996), 695-698
218.
V. A. Donchenko, Yu. A. Kreidun, A. V. Shapovalov, “Spontaneous soliton production by an optical pulse with a nonlinear shift of the carrier frequency”, Russian Physics Journal, 39:9 (1996), 815-819 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 14–19, September, 1996.
1995
219.
A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration of linear differential equations”, Theoret. and Math. Phys., 104:2 (1995), 921–934
220.
Yu. V. Kistenev, A. V. Shapovalov, “Dinamicheskaya neustoichivost opticheskikh kharakteristik rezonansnykh fraktalnykh struktur”, Zhurnal fizicheskoi khimii, 69:8 (1995), 1363-1367
221.
Yu. V. Kistenev, A. V. Shapovalov, “Absorbtsonnye svoistva rezonansnykh fraktalnykh sred”, Optika i spektroskopiya, 78:2 (1995), 260-265
222.
A. V. Shapovalov, I. V. Shirokov, Ya. V. Lisitsyn, V. I. Firstov, “Noncommutative four-dimensional subalgebras of conformal algebra integrable in the space R1,3”, Russian Physics Journal, 38:2 (1995), 209-212http://link.springer.com/article/10.1007/BF00560249
223.
O. L. Varaksin, V. V. Firstov, A. V. Shapovalov, I. V. Shirokov, “Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation: Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras”, Russian Physics Journal, 38:3 (1995), 299-303
224.
V. A. Donchenko, Yu. A. Kreidun, A. V. Shapovalov, “Propagation of a soliton-like pulse in a weakly nonlinear medium”, Russian Physics Journal, 38:4 (1995), 359-363http://link.springer.com/article/10.1007/BF00560098
225.
A. V. Shapovalov, I. V. Shirokov, Ya. V. Lisitsyn, V. I. Firstov, “Noncommutative 5-dimensional subalgebras of a conformal algebra integrable in R1,3”, Russian Physics Journal, 38:6 (1995), 641-645http://link.springer.com/article/10.1007/BF00559936
226.
O. L. Varaksin, V. V. Firstov, A. V. Shapovalov, I. V. Shirokov, “Quadratic algebras and noncommutative integration of Klein-Gordon equations in non-steckel Riemann spaces”, Russian Physics Journal, 38:5 (1995), 508-512 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 83–87, May, 1995. http://link.springer.com/article/10.1007/BF00559308
227.
Ya. V. Lisitsyn, A. V. Shapovalov, “Integration of the d'Alembert equation by means of four-dimensional nonabelian symmetry subalgebras with a single second-order operator”, Russian Physics Journal, 38:8 (1995), 804-807 , Translated from Izvestiya Vysshaya Uchebnykh Zavedenii, Fizika, No. 8, pp. 48–51, August, 1995. http://link.springer.com/article/10.1007/BF00559281
228.
Yu. A. Kreidun, A. V. Shapovalov, “Quadratic mapping with periodically disturbed parameter”, Russian Physics Journal, 38:10 (1995), 1099-1103 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 109–114, October, 1995. http://link.springer.com/article/10.1007/BF00559051
229.
A. V. Shapovalov, I. V. Shirokov, “Functional Algebras and Dimensional Reduction in the LPDEs Integration Problem”, Proceed. Int. Conf. “Symmetry in nonlinear mathematical physics” (Kiev, July 3-8), 4, Institute of Mathematics, NAN of Ukraine, Kiev, 1995, 62-68
1994
230.
Yu. V. Kistenev, A. V. Shapovalov, “Absorbtion of optical pulses under propagation through one-dimensional resonant fractal clusters”, Fractals, 2:4 (1994), 553-556
O. L. Varaksin, V. V. Firstov, A. V. Shapovalov, I. V. Shirokov, “Classification of F algebras and noncommutative integration of the Klein-Gordon equation in Riemannian spaces”, Russian Physics Journal, 36:1 (1993), 36-40 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 45–50, January, 1993. http://link.springer.com/article/10.1007/BF00559253
232.
A. V. Shapovalov, S. N. Yurchenko, “Using the complex WKB method for studying the evolution of initial pulses obeying the nonlinear Schrödinger equation”, Russian Physics Journal, 36:5 (1993), 431-437 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 19–25, May, 1993.
233.
M. D. Noskov, A. V. Shapovalov, “Transmission of quantum particles through a one-dimensional fractal potential barrier”, Russian Physics Journal, 36:7 (1993), 703-708 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 120–127, July, 1993. http://link.springer.com/article/10.1007/BF00559090
234.
V. A. Donchenko, Yu. V. Kistenev, M. D. Noskov, A. V. Shapovalov, “Interaction of electromagnetic waves with fractal structures”, Russian Physics Journal, 36:10 (1993), 955-964 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 76–87, October, 1993. http://link.springer.com/article/10.1007/BF00559160
235.
A. A. Drokin, A. V. Shapovalov, I. V. Shirokov, “Reduction and noncommutative integration of linear differential equations”, Russian Physics Journal, 36:11 (1993), 1059-1063 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 55–60, November, 1993. http://link.springer.com/article/10.1007/BF00560445
236.
A. V. Shapovalov, I. V. Shirokov, “Application of approximate symmetries to the construction of solutions of classical and quantum Hamiltonian systems”, Russian Physics Journal, 36:8 (1993), 806-808 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 114–117, August, 1993. http://link.springer.com/article/10.1007/BF00562038
237.
A.V. Shapovalov, I.V. Shirokov, Ya.V. Lisitsyn, “Metod nekommutativnogo integrirovaniya i kvantovye uravneniya Eilera na algebre Li so(4)”, Trudy V seminara"Gravitatsionnaya energiya i gravitatsionnye volny" (Dubna, 16-18 maya 1992), OIYaI, R2-92-55, Dubna, 1993, 186-190
1992
238.
A. V. Shapovalov, I. V. Shirokov, “Symmetry algebras of linear differential equations”, Theoret. and Math. Phys., 92:1 (1992), 697–703
239.
A. V. Shapovalov, S. N. Yurchenko, “Effect of initial pulse shape modulation on spontaneous soliton formation in the NSE model”, Russian Physics Journal, 35:6 (1992), 508-513 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 19–24, June, 1992 http://link.springer.com/article/10.1007/BF00559170
240.
A. V. Shapovalov, I. V. Shirokov, “Nonlinear Poisson bracket, F-algebras, and noncommutative integration of linear differential equations”, Russian Physics Journal, 35:7 (1992), 661-666 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 92–98, July, 1992 http://link.springer.com/article/10.1007/BF00559239
241.
Ya. V. Lisitsyn, A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration of quantum Euler equations on the Lie algebra so (4)”, Russian Physics Journal, 35:11 (1992), 1031-1036 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 45–50, November, 1992 http://link.springer.com/article/10.1007/BF00559099
1991
242.
V. G. Bagrov, A. V. Shapovalov, I. V. Shirokov, “Generation of new exactly solvable potentials of a nonstationary Schrödinger equation”, Theoret. and Math. Phys., 87:3 (1991), 635–640
243.
V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, “Separation of variables in the wave equation. Sets of the type (1.1) and Schrödinger equation”, Soviet Physics Journal, 34:2 (1991), 122-126 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 44–48, February, 1991. http://link.springer.com/article/10.1007/BF00940949
244.
V. G. Bagrov, B. V. Samsonov, A. V. Shapovalov, “Separation of variables in the wave equation. Sets of the type (1.1) and the algebra SU(1.2)”, Soviet Physics Journal, 34:2 (1991), 168-171 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 102–105, February, 1991. http://link.springer.com/article/10.1007/BF00940962
245.
A. V. Shapovalov, I. V. Shirokov, “Representations of Lie algebras and the problem of noncommutative integrability of linear differential equations”, Soviet Physics Journal, 34:4 (1991), 360-364 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 95–100, April, 1991 http://link.springer.com/article/10.1007/BF00898104
246.
V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, I. V. Shirokov, “Complete sets of symmetry operators containing a second-order operator and the problem of separation of variables in the wave equation”, Soviet Physics Journal, 34:4 (1991), 377-381 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 115–119, April, 1991. http://link.springer.com/article/10.1007/BF00898108
247.
V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, “Some problems of symmetry of the Schrödinger equations”, Soviet Physics Journal, 34:4 (1991), 382-385 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 120–123, April, 1991 http://link.springer.com/article/10.1007/BF00898109
248.
A. V. Shapovalov, I. V. Shirokov, “Noncqmmutative integration of Klein-Gordon and Dirac equations in Riemannian spaces with a group of motions”, Soviet Physics Journal, 34:5 (1991), 411-415 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 33–38, May, 1991 http://link.springer.com/article/10.1007/BF00897400
249.
V. G. Fedoseev, A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration of the Dirac equation in Riemann spaces possessing a group of automorphisms”, Soviet Physics Journal, 34:9 (1991), 777-781 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–46, September, 1991 http://link.springer.com/article/10.1007/BF00896710
250.
V. G. Bagrov, A. V. Shapovalov, I. V. Shirokov, “Enveloping algebra identities on solutions of conformally invariant wave equations”, Soviet Physics Journal, 34:9 (1991), 751-755 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 14–18, September, 1991 http://link.springer.com/article/10.1007/BF00896704
251.
V. G. Bagrov, A. V. Shapovalov, I. V. Shirokov, “Methods of generating integrable potentials for the Sochrödinger equation and nonlocal symmetries”, Soviet Physics Journal, 34:9 (1991), 755-761 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 19–25, September, 1991 http://link.springer.com/article/10.1007/BF0089670
252.
V. G. Bagrov, V. S. Mitkovskii, A. V. Shapovalov, “Konformno-shtekkelevy prostranstva vakuuma tipa (2.0).Metriki tipa N i 0 po Petrovu”, “Klassicheskie i kvantovostatisticheskie problemy relyativistskoi teorii gravitatsii”. Vsesoyuznaya gravitatsionnaya assotsiatsiya., Kazanskii gosudarstvennyi universistet, Kazan, 1991, 95-108
253.
V. G. Bagrov, A. V. Shapovalov, A. A. Yevseyvich, “Separation of variables in Dirac equation in Srackel Spaces.II. External gauge fields.”, Classical and Quantum Gravitity, 8:1 (1991), 163-173http://iopscience.iop.org/0264-9381/8/1/016
V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, I. V. Shirokov, “Identities on solutions of the wave equation in the enveloping algebra of the conformal group”, Theoret. and Math. Phys., 83:1 (1990), 347–353
255.
V. G. Bagrov, A. A. Yevseyevich, A. V. Shapovalov, “Separation of variables in the Dirac equation in Stackel spaces”, Classical and Quantum Gravitity, 7:4 (1990), 517-531http://iopscience.iop.org/0264-9381/7/4/004
A. V. Shapovalov, I. V. Shirokov, “Ob algebre simmetrii lineinogo differentsialnogo uravneniya”, “Sovremennyi gruppovoi analiz: Metody i prilozheniya. Nekotorye zadachi sovremennoi fiziki”, Vyp. 116, eds. A.V.Flegontov, LII AN, Leningrad, 1990, 52-58
257.
V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, I. V. Shirokov, “Subalgebras of the algebra of a conformal group with nontrivial center”, Soviet Physics Journal, 33:5 (1990), 416-419 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 45–48, May, 1990. http://link.springer.com/article/10.1007/BF00896080
258.
V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, I. V. Shirokov, “Commutative subalgebras of three first-order symmetry operators and separation of variables in the wave equation”, Sovet Physics Journal, 33:5 (1990), 448-452 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 79–84, May, 1990. http://link.springer.com/article/10.1007/BF00896088
259.
A. A. Nalivaiko, A. V. Shapovalov, “Evolyutsiya pryamougolnogo impulsa v ramkakh nelineinogo uravneniya Shredingera”, Izvestiya vuzov, Fizika, 33:7 (1990), 107-108
260.
V.G Bagrov, A.V Shapovalov, I.V Shirokov, “A new method of exact solution generation for the one-dimensional Schrödinger equation”, Physics Letters A, 147:7 (1990), 348–350http://dx.doi.org/10.1016/0375-9601(90)90551-X
V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, “Subalgebras of the Schrödinger algebra with nontrivial centers”, Soviet Physics Journal, 33:7 (1990), 553-556 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 5–9, July, 1990. http://link.springer.com/article/10.1007/BF00899100
262.
V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, “Free Schrödinger equation analyzed in terms of the wave equation”, Soviet Physics Journal, 33:7 (1990), 600-604 , Translated from Izvestiya Vysshikh uchebnykh Zavedenii, Fizika, No. 7, pp. 59–64, July 1990. http://link.springer.com/article/10.1007/BF00899111
263.
V. G. Bagrov, A. A. Evseevich, A. V. Shapovalov, “Tochnye resheniya uravneniya Diraka v klasse shtekkelevykh prostranstv tipa (2.1)”, Trudy II seminara “Gravitatsionnaya energiya i gravitatsionnye volny”, R 2-90-245, OIYaI, Dubna, 1990, 117-123
264.
V. G. Bagrov, A. A. Evseevich, A. V. Shapovalov, “Razdelenie peremennykh v uravnenii Diraka v prostranstvakh Shtekkelya”, Gravitatsiya i obschaya teoriya otnositelnosti, No 27, Kazanskii gosudarstvennyi universistet, Kazan, 1990, 55-79
265.
V. G. Bagrov, A. V. Shapovalov, I. V. Shirokov, “Novyi klass tochnykh reshenii uravneniya Shredingera i nelokalnye simmetrii”, “Gravitatsiya i elektromagnetizm”, vyp. 5, “Universitetskoe”, Minsk, 1990, 12-15
1989
266.
É. V. Lugin, A. V. Shapovalov, “Propagation of optical pulses at an absorption line in the presence of a weak nonlinearity”, Soviet Physics Journal, 32:2 (1989), 106-109 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 36–39, February, 1989 http://link.springer.com/article/10.1007/BF00898669
267.
A. A. Evseevich, A. V. Shapovalov, “Classification of the Dirac equation with an external SU(3) gauge field admitting a first-order symmetry operator of special type”, Sovet Physics Journal, 32:6 (1989), 427-431 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 22–21, June, 1989 http://link.springer.com/article/10.1007/BF00898623
268.
V. G. Bagrov, A. V. Shapovalov, A. A. Evseevich, “Yang-Mills fields permitted by abelian complete sets of first-order symmetry operators of the Dirac equation”, Soviet Physics Journal, 32:10 (1989), 781-784 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 30–34, October, 1989. http://link.springer.com/article/10.1007/BF00898306
269.
V. A. Donchenko, M. V. Kabanov, E. V. Lugin, A. A. Nalivaiko, A. V. Shapovalov, “Effekty vzaimodeistviya opticheskikh impulsov v slabo nelineinoi pogloschayuschei srede”, Optika atmosfery, 2:12 (1989), 1286-1290
270.
V. G. Bagrov, A. V. Shapovalov, I. V. Shirokov, “Metod generatsii novykh tochnykh reshenii odnomernogo uravneniya Shredingera”, Izvestiya vuzov, Fizika, 32:11 (1989), 112-114
271.
V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, I. V. Shirokov, “Algebraicheskie svoistva volnovogo uravneniya i problema razdeleniya peremennykh”, “Gravitatsiya i elektromagnetizm”, vyp. 4, “Universitetskoe”, Minsk, 1989, 20-34
272.
V.G. Bagrov, B.F. Samsonov, A.V. Shapovalov, I.V. Shirokov, “Simmetriya i razdelenie peremennykh v uravnenii Dalambera”, “Sovrem.gruppovoi analiz: Metody i prilozheniya”, Elm, Baku, 1989, 32-36
1988
273.
V. A. Donchenko, M. V. Kabanov, E. V. Lugin, A. A. Nalivaiko, A. V. Shapovalov, “O formirovanii opticheskikh impulsov v linii pogloscheniya slabo nelineinoi sredy”, Optika atmosfery, 1:1 (1988), 67-72
274.
V. S. Mitkovskii, A. V. Shapovalov, “Konformnoe otobrazhenie prostranstv Shtekkelya na prostranstva Einshteina. Postanovka zadachi i nekotorye klassy prostranstv tipa (2.0)”, “Gravitatsiya i elektromagnetizm”, Universitetskoe, Minsk, 1988, 155-162
275.
V. A. Donchenko, M. V. Kabanov, E. V. Lugin, A. A. Nalivaiko, A. V. Shapovalov, “O vozmozhnom formirovanii ustoichivykh impulsov v slabo nelineinoi srede”, “Nelineinaya optika i optoakustika atmosfery”, TF SO AN SSSR, Tomsk, 1988, 119-123
276.
V. G. Bagrov, A. A. Evseevich, A. V. Shapovalov, Razdelenie peremennykh v uravnenii Diraka v prostranstvakh Shtekkelya tipov (2.0), (2.1), Preprint N9, TF SO AN SSSR, Tomsk, 1988 , 43 pp.
1987
277.
E. V. Lugin, A. V. Shapovalov, “Rasprostranenie svetovykh impulsov spetsialnoi formy v srede s pogloscheniem”, Izvestiya vuzov, Fizika, 37:9 (1987), 102-104
1986
278.
V. G. Bagrov, A. V. Shapovalov, “Symmetry of the Dirac equation with an external non-Abelian gauge field”, Soviet Physics Journal, 29:3 (1986), 235-242 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 95–103, March, 1986. http://link.springer.com/article/10.1007/BF00891885
V. G. Bagrov, V. V. Obukhov, A. V. Shapovalov, “Spetsialnye shtekkelevy prostranstva elektrovakuuma”, Gravitatsiya i obschaya teoriya otnositelnosti, Vyp. 23, Kazanskii gosudarstvennyi universistet, Kazan, 1986, 10-30
281.
V. G. Bagrov, V. V. Obukhov, A. V. Shapovalov, “Polya tyagoteniya v probleme Vaidya, dopuskayuschie razdelenie peremennykh v uravnenii Gamiltona-Yakobi”, Izvestiya vuzov, Fizika, 29:10 (1986), 3-8
282.
V. G. Bagrov, V. V. Obukhov, A. V. Shapovalov, “Gravitation field in the Vaidya problem allowing separation of variables in the Hamilton-Jacobi equation”, Soviet Physics Journal, 29:10 (1986), 775-779 , ranslated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 3–8, October, 1986. http://link.springer.com/article/10.1007/BF00900736
283.
V. G. Bagrov, V. V. Obukhov, K. E. Osetrin, A. V. Shapovalov, “Elektrovakuumnye prostranstva Shtekkelya-Vaidya tipa (n.1)”, Problemy gravitatsii, Moskovskii gosudarstvennyi universitet, Moskva, 1986, 159-167
284.
V. F. Konusov, A. A. Vaal, A. V. Shapovalov, Osnovy teorii konechnykh grupp dlya fizikov (Uchebnoe posobie), Tomskii gosudarstvennyi universitet, Tomsk, pr. Lenina, 36, 1986 , 190 pp.
1984
285.
V. G. Bagrov, V. V. Obukhov, A. V. Shapovalov, “Special Stâckel spaces of the electrovacuum”, Soviet Physics Journal, 27:8 (1984), 645-647 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 20–22, August, 1984. http://link.springer.com/article/10.1007/BF00893103
1983
286.
V. G. Bagrov, V. V. Obukhov, A. V. Shapovalov, “Shtekkelevy prostranstva elektrovakuuma s dvukhparametricheskoi abelevoi gruppoi dvizhenii. Nabor tipa (2.1)”, Izvestiya vuzov, Fizika, 26:1 (1983), 6-10
287.
V. G. Bagrov, V. V. Obukhov, A. V. Shapovalov, “Stueckel spaces of the electrovacuum with two-parameter Abelian group of motions. Formulation of the problem and sets of the type (2.1)”, Soviet Physics Journal, 26:1 (1983), 4-8 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 6–10, January 1983. http://link.springer.com/article/10.1007/BF00892169
288.
V. G. Bagrov, V. V. Obukhov, A. V. Shapovalov, “Stueckel spaces of the electrovacuum with a two-parameter Abelian group of motions. Set of the type (2.0)”, Soviet Physics Journal, 26:3 (1983), 313-317 , Translated from Izvestiya Vysshih Uchebnykh Zavedenii, Fizika, No. 3, pp. 115–120, March, 1983. http://link.springer.com/article/10.1007/BF00895153
289.
V. G. Bagrov, V. V. Obukhov, A. V. Shapovalov, “Shtekkelevy prostranstva elektrovakuuma s dvukhparametricheskoi abelevoi gruppoi dvizhenii”, Izvestiya vuzov, Fizika, 26:12 (1983), 104-106
1981
290.
V. G. Bagrov, V. V. Obukhov, A. V. Shapovalov, “O polyakh III tipa po klassifikatsii Petrova”, Izvestiya vuzov, Fizika, 24:10 (1981), 102-103
1980
291.
V. V. Obukhov, A. V. Shapovalov, Obukhov V.V., Shapovalov A.V. O neterovskikh dopustimykh operatorakh i zakonakh sokhraneniya uravneniya Sin-Gordon, Rukopis deponirovana v VINITI Reg. N2242-80 Dep. (18 s.), 1980
1978
292.
V. G. Bagrov, D. M. Gitman, V. N. Zadorozhnyi, A. V. Shapovalov, V. N. Shapovalov, “New exact solutions of the Dirac equation. IX”, Soviet Physics Journal, 21:3 (1978), 304-307 , Translated from Izvestiya Vysshikh Uchebenykh Zavedenii, Fizika, No. 3, pp. 46–49, March, 1978. http://link.springer.com/article/10.1007/BF00894722
1979
293.
A. V. Shapovalov, “Finite-dimensional irreducible representations of Hamiltonian Lie superalgebras”, Math. USSR-Sb., 35:4 (1979), 541–554
1977
294.
V. G. Bagrov, D. M. Gitman, A. V. Shapovalov, “Integrals of the motion for an electron in a quantized plane electromagnetic wave”, Soviet Physics Journal, 20:2 (1977), 233-237 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 116-121, February, 1977. Original article submitted May 28, 1976. http://link.springer.com/article/10.1007/BF01297392
295.
V. G. Bagrov, D. M. Gitman, A. V. Shapovalov, V. N. Shapovalov, “New exact solutions of the Dirac equations. VI”, Soviet Physics Journal, 20:6 (1977), 783-790 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 105–114, June, 1977. http://link.springer.com/article/10.1007/BF00892767
296.
V. G. Bagrov, D. M. Gitman, N. B. Sukhomlin, A. V. Shapovalov, V. N. Shapovalov, “New exact solutions of the Dirac equation. VII”, Soviet Physics Journal, 20:7 (1977), 871-876 , Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–51, July, 1977. http://link.springer.com/article/10.1007/BF00893130
1976
297.
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