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Kalyakin, Leonid Anatol'evich

Total publications: 84 (81)
in MathSciNet: 64 (62)
in zbMATH: 50 (50)
in Web of Science: 41 (40)
in Scopus: 37 (37)
Cited articles: 55
Citations in Math-Net.Ru: 250
Citations in Web of Science: 150
Citations in Scopus: 97
Presentations: 1

Number of views:
This page:2416
Abstract pages:12996
Full texts:3428
References:1409
Kalyakin, Leonid Anatol'evich
Professor
Doctor of physico-mathematical sciences (1988)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 8.07.1947
Phone: +7 (347) 273 33 42
Fax: +7 (347) 272 59 36
E-mail:
Website: http://matem.anrb.ru/ru/kalyakinla
Keywords: asymptotics, small parameter, differential equations, resonance.
UDC: 517.928.226, 517.946.9, 517.948, 517.956, 517.956.226, 517.958.530.145.7, 518, 519.634
MSC: 35C20, 35B40, 35L40, 35L70, 35Q55

Subject:

Asymptotic solutions of nonlinear differential equations.

Biography

1969 Mathematician diploma, Ural State University, Sverdlovsk. From 1968 work in the Institute of Mathematics and Mechanics, Ural Branch of RAS, Sverdlovsk. 1975 PhD, thesis "Methods of solving unstable problems", Ural State University, Sverdlovsk. From 1978 work in the Department of Physics and Mathematics, Bashkir Scientific center of RAS. From 1987 Head of the Department of Differential Equations, Institute of Mathematics, Ufa Scientific Center of RAS. 1989 Doctor's degree, thesis "Long-wave asymptotics for the solutions of the systems of nonlinear equations", Institute of Mathematics and Mechanics, Ural Branch of RAS, Sverdlovsk. 1992 Professor of the Department of differential Equations, Bashkir State University, 2000 Soros' Professor, supervisor of six philosophy doctors in differential equations. For many years gives the lecture courses on differential equations and mathematical physics at the Faculty of Mathematics, BSU. Scientific interests are concerned to the application of asymptotic methods for solving nonlinear problems of mathematical physics. Author of more than 80 publications. Co-author of papers concerning to application of asymptotic methods in chemical kinetics, fluid dynamics, written in active collaboration with chemists, physicists and mechanicians.

   
Main publications:
  1. L. A. Kalyakin, “Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems”, Russian Math. Surveys, 44:5 (1989), 1–34
  2. L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Russian Math. Surveys, 63:5 (2008), 791–857

http://www.mathnet.ru/eng/person8331
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/203746

Full list of publications:
| by years | by types | by times cited in WoS | by times cited in Scopus | scientific publications | common list |



   2018
1. L. A. Kalyakin, “Resonance capture in a system of two oscillators near equilibrium”, Theoret. and Math. Phys., 194:3 (2018), 331–346  mathnet  crossref  crossref  isi  elib  scopus
2. L. A. Kalyakin, “Analysis of a Mathematical Model for Nuclear Spins in an Antiferromagnet”, Russian Journal of Nonlinear Dynamics, 14:2 (2018), 217–234 http://nd.ics.org.ru/authors_nd/detail/26267-leonid_kalyakin  mathnet  crossref  elib
3. J. A. Baimova, I, Evazzade, L. A. Kalyakin, S. V. Dmitriev and K. Zhou, “Dehydrogenation of graphane by external driving”, IOP Conf. Series: Materials Science and Engineering, 447:conference 1 (2018), 012011 , 5 pp.  crossref  scopus
4. L. A. Kalyakin, “Capture and holding of resonance far from equilibrium”, Ufa Math. J., 10:4 (2018), 64–76  mathnet  crossref  isi

   2017
5. L. A. Kalyakin, “Asymptotic analysis of the model of gyromagnetic autoresonance”, Comput. Math. Math. Phys., 57:2 (2017), 281–296  mathnet  crossref  crossref  isi (cited: 2)  elib  scopus (cited: 1)
6. L. A. Kalyakin, “Adiabatic approximation for a Model of Cyclotron Motion”, Math. Notes, 101:5 (2017), 850–862  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
7. L. A. Kalyakin, “Painleve II equation as a model of a resonant interaction of oscillators”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 2, 2017, 104–116  mathnet  crossref  isi  elib
8. Kalyakin L.A, “Adiabatic approximation in a resonance capture problem”, Ufa Mathematical Journal, 9:3 (2017), 61-75 http://matem.anrb.ru/en/article?art_id=461  mathnet  crossref  mathscinet  isi  elib  scopus
9. S. A. Kordyukova, L. A. Kalyakin, “On a double boundary layer in a nonlinear boundary value problem”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 129–146  mathnet  crossref  mathscinet  isi  elib  scopus

   2016
10. L. A. Kalyakin, “Stability of the autoresonance in a dissipative system”, Russian Journal of Mathematical Physics, 23:1 (2016), 77–87  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
11. L. A. Kalyakin, “Stability of equilibrium with respect to a white noise”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 68–77  mathnet  crossref  mathscinet  elib

   2015
12. L. A. Kalyakin, “Lyapunov Functions in Justification Theorems for Asymptotics”, Math. Notes, 98:5 (2015), 752–764  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
13. L.A.Kalyakin, “Asimptoticheskii analiz modeli tsiklotronnogo giromagnitnogo avtorezonansa”, Vestnik chelyabinskogo gosudarstvennogo universiteta, 22 (377), Fizika:21 (2015), 68-74 http://www.lib.csu.ru/vch/377/vcsu15_22.pdf  elib

   2014
14. L. A. Kalyakin, “Phantom asymptotic solutions”, Ufa Math. Journal, 6:2 (2014), 44–65  mathnet  crossref  elib  elib  scopus (cited: 1)
15. L. A. Kalyakin, “Synchronization in a nonisochronous nonautonomous system”, Theoret. and Math. Phys., 181:2 (2014), 1339–1348  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 1)  elib  elib  scopus (cited: 2)
16. L. A. Kalyakin, “Lyapunov functions in barriers for parabolic equations and in stability problems with respect to “white noise””, Russian Journal of Mathematical Physics, 21:4 (2014), 472–483 http://link.springer.com/article/10.1134/S1061920814040050  crossref  mathscinet  zmath  isi (cited: 2)
17. L. A. Kalyakin, “Existence Theorems and Estimates of Solutions for Equations of Principal Resonance”, Journal of Mathematical Sciences, 200:1 (2014), 82-95 http://link.springer.com/search/page/3?query=Kalyakin#page-1  crossref  mathscinet  zmath  scopus (cited: 2)
18. L Kalyakin, “Stability under persistent perturbation by white noise”, Journal of Physics: Conference Series, 482 (2014), 012019 , 7 pp.  crossref  mathscinet  isi (cited: 4)

   2013
19. L. A. Kalyakin, “Stability of nondissipative systems under random perturbations that are small in the mean”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 2, 2013, 170–178  mathnet  mathscinet  elib
20. L. A. Kalyakin, O. A. Sultanov, “Stability of autoresonance models”, Differential Equations, 49:3 (2013), 267–281 http://www.gproxx.com/http://link.springer.com/article/10.1134/S0012266113030014  crossref  mathscinet  zmath  elib

   2012
21. L. A. Kalyakin, “Stability of Nondissipative Systems under Persistent Random Perturbations”, Math. Notes, 92:1 (2012), 136–139  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)

   2013
22. L. A. Kalyakin, “Analysis of the Bloch equations for the nuclear magnetization model”, Proceedings of the Steklov Institute of Mathematics, 281:Suppl. 1 (2013), 64–81  mathnet  crossref  isi  elib  scopus (cited: 1)

   2012
23. L. A. Kalyakin, “Asymptotic analysis of the surfing acceleration model”, Ufimsk. Mat. Zh., 4:2 (2012), 101–113  mathnet  elib

   2011
24. L. A. Kalyakin, O. A. Sultanov, M. A. Shamsutdinov, “Asymptotic analysis of a model of nuclear magnetic autoresonance”, Theoret. and Math. Phys., 167:3 (2011), 762–771  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 2)  elib  scopus (cited: 3)
25. A.T. Kharisov, L.A. Kalyakin, M.A. Shamsutdinov, “Autoresonance Excitation of Nonlinear Oscillations of Magnetization and Domain Walls in Ferromagnets”, Solid State Phenomena, 168-169 (2011), 77-80 http://www.scientific.net/SSP.168-169.77  crossref  isi
26. V.N. Nazarov, L.A. Kalyakin, M.A. Shamsutdinov, “Autoresonance Parametric Excitation of the Magnetic Breather in a Uniaxial Ferromagnet”, Solid State Phenomena, 168-169 (2011), 81-84 http://www.scientific.net/SSP.168-169.81  crossref  isi (cited: 1)
27. O. A. Sultanov, L. A. Kalyakin, “Averaging of the Bloch equations”, Vestnik Chelyabinsk. Gos. Univ., 2011, no. 14, 107–112  mathnet  mathscinet  elib
28. L. A. Kalyakin, V. Yu. Novokshenov, I. T. Habibullin, E. G. Ekomasov, A. T. Kharisov, “In memory of Miniakhat Asgatovich Shamsutdinov”, Ufimsk. Mat. Zh., 3:1 (2011), 122–123  mathnet

   2010
29. L. A. Kalyakin, “Analysis of a synchronization model in an anisochronous system”, Comput. Math. Math. Phys., 50:8 (2010), 1338–1349  mathnet  crossref  mathscinet  adsnasa  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)

   2009
30. L. A. Kalyakin, M. A. Shamsutdinov, “Autoresonant asymptotics in an oscillating system with weak dissipation”, Theoret. and Math. Phys., 160:1 (2009), 960–967  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 8)  elib
31. L. A. Kalyakin, “Averaging method for the problems on asymptotics at infinity”, Ufimsk. Mat. Zh., 1:2 (2009), 29–52  mathnet  zmath  elib

   2008
32. L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Russian Math. Surveys, 63:5 (2008), 791–857  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 35)  elib (cited: 19)  elib (cited: 19)  scopus (cited: 26)

   2007
33. L. A. Kalyakin, M. A. Shamsutdinov, “Adiabatic approximations for Landau–Lifshitz equations”, Proc. Inst. Math. Mech., 259, suppl. 2 (2007), S124–S140  mathnet  crossref  elib  scopus (cited: 3)
34. E. M. Maslov, L. A. Kalyakin, A. G. Shagalov, “Breather resonant phase locking by an external perturbation”, Theoret. and Math. Phys., 152:2 (2007), 1173–1182  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 7)  elib  scopus (cited: 6)
35. R. N. Garifullin, L. A. Kalyakin, M. A. Shamsutdinov, “Autoresonance excitation of a breather in weak ferromagnetics”, Comput. Math. Math. Phys., 47:7 (2007), 1158–1170  mathnet  crossref  mathscinet  elib (cited: 6)  elib (cited: 6)  scopus (cited: 10)

   2008
36. L. A. Kalyakin, Yu. Yu. Bagderina, “Asymptotics for the solution of averaged equations for the system of coupled oscillators”, J. Math. Sci., 151:1 (2008), 2699–2709  mathnet  crossref  mathscinet  zmath  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)

   2006
37. L. A. Kalyakin, “Intermediate asymptotics for solutions to the degenerate principal resonance equations”, Comput. Math. Math. Phys., 46:1 (2006), 79–89  mathnet  crossref  mathscinet  zmath  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)

   2005
38. L. A. Kalyakin, Yu. Yu. Bagderina, “Asymptotics of Bounded-at-Infinity Solutions of the Principal Resonance Equation”, Math. Notes, 78:1 (2005), 76–87  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
39. L. A. Kalyakin, “Resonance Capture in a Nonlinear System”, Theoret. and Math. Phys., 144:1 (2005), 944–951  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib  scopus (cited: 2)
40. L. Kalyakin, “Asymptotic analysis of a model of autoresonance”, International Conference on Control and Synchronzation of Dynamical Systems (OCTOBER 4-7 2005 León Gto.México), Journal of Physics: Conference Series, 23, 2005, 17–22  crossref  scopus (cited: 1)

   2004
41. L. A. Kalyakin, “Asymptotic Solution of the Threshold Phenomenon Problem for the Principal Resonance Equations”, Differ. Equ., 40:6 (2004), 780–788  mathnet  crossref  mathscinet

   2003
42. L. A. Kalyakin, “Averaging in the Autoresonance Model”, Math. Notes, 73:3 (2003), 414–418  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 8)  scopus (cited: 4)
43. L. A. Kalyakin, “Justification of asymptotic expansions for the principal resonance equations”, Proc. Inst. Math. Mech., 2003no. , suppl. 1, S108–S122  mathnet  mathscinet  zmath  elib
44. L. A. Kalyakin, “Asymptotic Behavior of Solutions of Equations of Main Resonance”, Theoret. and Math. Phys., 137:1 (2003), 1476–1484  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 7)  scopus (cited: 6)
45. V. M. Babich, L. A. Kalyakin, M. D. Ramazanov, N. Kh. Rozov, “Arlen Mikhailovich Il'in (on the occasion of the 70th anniversary)”, Proc. Inst. Math. Mech., 2003no. , suppl. 1, S1–S7  mathnet  mathscinet  zmath  elib

   2002
46. L. A. Kalyakin, “Asymptotic Solution of the Autoresonance Problem”, Theoret. and Math. Phys., 133:3 (2002), 1684–1691  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
47. V. M. Babich, R. R. Gadyl'shin, A. R. Danilin, S. Yu. Dobrokhotov, V. A. Il'in, L. A. Kalyakin, E. F. Mishchenko, V. Yu. Novokshenov, Yu. S. Osipov, M. D. Ramazanov, N. Kh. Rozov, V. A. Sadovnichii, “Arlen Mikhailovich Il'in (A tribute in honor of his 70th birthday)”, Differ. Equ., 38:8 (2002), 1075–1080  mathnet  crossref  mathscinet

   2001
48. L. A. Kalyakin, “Weak perturbations of solutions with movable singularities”, Proc. Inst. Math. Mech., 2001no. , suppl. 1, S85–S106  mathnet  mathscinet  zmath  elib
49. L. A. Kalyakin, “Perturbation of Solutions with Moving Singularities”, Theoret. and Math. Phys., 127:3 (2001), 751–759  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus

   2000
50. L. A. Kalyakin, “Asymptotic decay of solutions of the Liouville equation under perturbations”, Math. Notes, 68:2 (2000), 173–184  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus

   1999
51. L. A. Kalyakin, “Perturbation of a singular solution to the Liouville equation”, Theoret. and Math. Phys., 118:3 (1999), 307–313  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
52. L. A. Kalyakin, M. M. Shakiryanov, “Asymptotic behavior of the solution of the Cauchy problem for the two-dimensional homogeneous wave equation”, Differ. Equ., 35:9 (1999), 1307–1309  mathnet  mathscinet

   1998
53. L. A. Kalyakin, “Week interaction of the perturbed Korteveg–de Vries solutions”, Fundam. Prikl. Mat., 4:4 (1998), 1179–1205  mathnet  mathscinet  zmath

   1997
54. L. A. Kalyakin, S. I. Maslennikov, “Method of the asymptotic approximations to the mathematical analysis of the chemical kinetic problem”, Matem. Mod., 9:8 (1997), 60–69  mathnet  mathscinet  zmath
55. L. A. Kalyakin, V. A. Lazarev, “Perturbation of the two-soliton solution of the KdV equation”, Theoret. and Math. Phys., 112:1 (1997), 866–874  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 2)  scopus (cited: 2)

   1996
56. A. I. Bobenko, A. M. Il'in, S. Yu. Dobrokhotov, A. R. Its, L. A. Kalyakin, V. B. Matveev, V. Yu. Novokshenov, A. B. Shabat, “Ramil' Faritovich Bikbaev (obituary)”, Russian Math. Surveys, 51:1 (1996), 129–133  mathnet  crossref  crossref  mathscinet  adsnasa  isi

   1995
57. L. A. Kalyakin, “Asymptotics of the first correction in the perturbation of the $N$-soliton solution to the KdV equation”, Math. Notes, 58:2 (1995), 814–823  mathnet  crossref  mathscinet  zmath  isi (cited: 2)
58. L. A. Kalyakin, “On the problem of first correction in soliton perturbation theory”, Sb. Math., 186:7 (1995), 977–1002  mathnet  crossref  mathscinet  zmath  isi

   1994
59. L. A. Kalyakin, S. G. Glebov, “On the solvability of nonlinear equations of Shrödinger type in the class of rapidly oscillating functions”, Math. Notes, 56:1 (1994), 673–678  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)

   1993
60. L. A. Kalyakin, “Asymptotics of a double integral of Fourier type in the theory of soliton perturbation”, Differ. Equ., 29:6 (1993), 867–880  mathnet  mathscinet

   1992
61. L. A. Kalyakin, “Perturbation of the Korteweg–de Vries soliton”, Theoret. and Math. Phys., 92:1 (1992), 736–747  mathnet  crossref  mathscinet  zmath  isi (cited: 10)  scopus (cited: 10)

   1991
62. L. A. Kalyakin, “Asymptotics of an integral that arises in the theory of perturbations of KdV solitons”, Math. Notes, 50:5 (1991), 1114–1122  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)

   1990
63. L. A. Kalyakin, “The method of matching in a problem on long-wave modulation of nonlinear two-dimensional waves with dispersion”, Tr. Mosk. Mat. Obs., 53, MSU, M., 1990, 3–41  mathnet  mathscinet  zmath

   1989
64. L. A. Kalyakin, “Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems”, Russian Math. Surveys, 44:1 (1989), 3–42  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 41)

   1988
65. L. A. Kalyakin, “Local resonance in a weakly nonlinear problem”, Mat. Zametki, 44:5 (1988), 697–699  mathnet  zmath
66. L. A. Kalyakin, “Asymptotic transitions from discrete to continuous models”, Theoret. and Math. Phys., 76:3 (1988), 891–894  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 2)
67. L. A. Kalyakin, “Asymptotic decay of a one-dimensional wave packet in a nonlinear dispersive medium”, Math. USSR-Sb., 60:2 (1988), 457–483  mathnet  crossref  mathscinet  zmath

   1987
68. L. A. Kalyakin, Differ. Uravn., 23:4 (1987), 696–705  mathnet  mathscinet

   1986
69. L. A. Kalyakin, “Asymptotic integration of a perturbed hyperbolic system of equations in the class of conditionally periodic functions”, Tr. Mosk. Mat. Obs., 49, MSU, M., 1986, 56–70  mathnet  mathscinet  zmath

   1984
70. L. A. Kalyakin, “The asymptotic behaviour of the solution of a hyperbolic system of equations with a non-linear perturbation”, Russian Math. Surveys, 39:5 (1984), 277–278  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)

   1985
71. L. A. Kalyakin, “Long wave asymptotics of asolution of a hyperbolic system of equations”, Math. USSR-Sb., 52:1 (1985), 91–114  mathnet  crossref  mathscinet  zmath

   1984
72. L. A. Kalyakin, Differ. Uravn., 20:2 (1984), 351–353  mathnet  zmath

   1983
73. L. A. Kalyakin, “An asymptotic expansion of the solution of a degenerate parabolic equation with a small parameter”, Russian Math. Surveys, 38:1 (1983), 194–195  mathnet  crossref  mathscinet  zmath  adsnasa  isi
74. L. A. Kalyakin, Differ. Uravn., 19:11 (1983), 1991–1992  mathnet  mathscinet  zmath
75. L. A. Kalyakin, Differ. Uravn., 19:4 (1983), 628–644  mathnet  mathscinet  zmath

   1982
76. L. A. Kalyakin, Differ. Uravn., 18:10 (1982), 1724–1738  mathnet  mathscinet  zmath

   1979
77. L. A. Kalyakin, Differ. Uravn., 15:4 (1979), 668–680  mathnet  mathscinet  zmath
78. L. A. Kalyakin, Differ. Uravn., 15:10 (1979), 1873–1887  mathnet  mathscinet

   1976
79. L. A. Kalyakin, “On approximate methods of solving nonlinear boundary value problems with a small parameter”, Math. USSR-Sb., 28:4 (1976), 491–500  mathnet  crossref  mathscinet  zmath  isi

   1974
80. L. A. Kalyakin, Differ. Uravn., 10:9 (1974), 1684–1691  mathnet  mathscinet  zmath

   1972
81. L. A. Kalyakin, “Approximate solution of certain unstable problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 1972, no. 10, 41–45  mathnet  mathscinet  zmath
82. L. A. Kalyakin, “The approximate solution of ill-posed problems in normed spaces”, U.S.S.R. Comput. Math. Math. Phys., 12:5 (1972), 104–122  mathnet  crossref  mathscinet  zmath  scopus

   1971
83. L. A. Kalyakin, “Galerkin's method for equations with a small parameter in the highest order derivatives”, Math. USSR-Sb., 14:4 (1971), 525–536  mathnet  crossref  mathscinet  zmath

   1969
84. L. A. Kalyakin, “Ritz method for equations with small parameters for higher derivatives”, Math. Notes, 6:1 (1969), 513–516  mathnet  crossref  mathscinet  zmath  scopus

Presentations in Math-Net.Ru
1. Asymptotic analysis of autoresonance in the system with small dissipation
L. A. Kalyakin
International conference "Geometrical Methods in Mathematical Physics"
December 14, 2011 16:00   

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