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Zhiber, Anatoly Vasilievich

Total publications: 38 (31)
in MathSciNet: 21 (21)
in zbMATH: 14 (14)
in Web of Science: 8 (8)
in Scopus: 6 (6)
Cited articles: 21
Citations in Math-Net.Ru: 307
Citations in Web of Science: 149
Citations in Scopus: 86

Number of views:
This page:3011
Abstract pages:9110
Full texts:3548
References:698
Professor
Doctor of physico-mathematical sciences (1994)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 18.06.1946
E-mail:
Keywords: dynamical systems, Lie–Backlund groups, integrability of hyperbolic systems, equation of Liouville type.

Subject:

Complete lists of Klein-Gordon equations and their generalizations were obtained possessing higher symmetries. An effective criterion of Darboux integrability of differential equations was established in terms of the Laplace invariants. The classical problem of the classification of nonlinear hyperbolik equations possessing integrals was solved. A new method of integration of such equations was suggested.

Biography

Graduated from Faculty of Mathematics and Mechanics of Novosibirsk State University (NSU) in 1969 (department of differential equations). Ph.D. thesis was defended in 1975. D.Sci. thesis was defended in 1994. A list of my works contains more than 50 titles.

   
Main publications:
  1. A.V. Zhiber, “Kvazilineinye giperbolicheskie uravneniya s beskonechnomernoi algebroi simmetrii”, Izvestiya RAN, ser. matem., 58:4 (1994), 33–54  mathnet  mathscinet  zmath
  2. V.V. Sokolov, A.V. Zhiber, “On the Darboux integrate hyperbolik equation”, Phys. Letters A, 208 (1995), 303–308  crossref  mathscinet  zmath  adsnasa
  3. A.V. Zhiber, V.V. Sokolov, “Novyi primer giperbolicheskogo uravneniya obladayuschego integralami”, TMF, 120:1 (1999), 20–26  mathnet  mathscinet  zmath
  4. A.V. Zhiber, V.V. Sokolov, “Tochno integriruemye giperbolicheskie uravneniya liuvillevskogo tipa”, UMN, 56:1, 63–106  mathnet  mathscinet  zmath

http://www.mathnet.ru/eng/person9184
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/189941

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



   2020
1. R. N. Gaisina, A. V. Zhiber, “O zakonakh sokhraneniya dlya odnogo klassa evolyutsionnykh sistem uravnenii”, Vestnik BashGU, 25:1 (2020), 4–11
2. A. B. Zhiber, G. Z. Murtazina, N. A. Sidelnikova, Osnovnye differentsialnye uravneniya matematicheskoi fiziki, RITs BashGU, Ufa, 2020 , 303 pp.
3. V. E. Adler, P. Winternitz, R. N. Garifullin, A. V. Zhiber, D. Levi, A. V. Mikhailov, I. Kh. Musin, F. W. Nijhoff, V. V. Sokolov, B. I. Suleimanov, E. V. Ferapontov, A. P. Fordy, I. T. Habibullin, I. Yu. Cherdantsev, R. A. Sharipov, R. S. Yulmukhametov, “In memory of Yamilov Ravil Islamovich”, Ufa Math. J., 12:3 (2020), 119–120  mathnet

   2019
4. A. V. Zhiber, N. M. Tsirelman, “Determining temperature fields in a spatially inhomogeneous nonlinear medium”, Complex Analysis. Mathematical Physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 162, VINITI, Moscow, 2019, 34–41  mathnet  mathscinet
5. A. V. Zhiber, A. M. Yureva, “Special class of Liouville-type hyperbolic equations”, J. Math. Sci., 236:6 (2019), 594–602  crossref  mathscinet  zmath  scopus

   2018
6. A. V. Zhiber, A. M. Yur'eva, “On a Certain Class of Hyperbolic Equations with Second-order Integrals”, Mathematical physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 152, VINITI, Moscow, 2018, 46–52  mathnet  mathscinet
7. A. V. Zhiber, G. Z. Mukhametova, N. A. Sidelnikova, Kraevye zadachi dlya osnovnykh tipov uravnenii matematicheskoi fiziki, RITs BashGU, Ufa, 2018 , 295 pp., ISBN 978-5-7477-4861-3

   2019
8. A. V. Zhiber, A. M. Yur'eva, “Special class of of Liouville-type hyperbolic equations”, J. Math. Sci. (N. Y.), 236:6 (2019), 594–602  mathnet  crossref  mathscinet  zmath  scopus

   2017
9. A. V. Zhiber, D. R. Toshmurodova, “Kharakteristicheskie koltsa Li giperbolicheskikh sistem uravnenii, porozhdennykh uravneniem Penleve II”, Sovremennaya matematika i ee prilozheniya, Materialy Mezhdunarodnoi nauchno-prakticheskoi konferentsii (Ufa, 18–20 maya 2017 g.), RITs BashGU, Ufa, 2017, 328–332
10. A. V. Zhiber, R. D. Murtazina, I. T. Khabibullin, A. B. Shabat, Uravneniya matematicheskoi fiziki. Nelineinye integriruemye uravneniya, Uchebnoe posobie dlya bakalavriata i magistratury, Universitety Rossii, 2-e izd., Izdatelstvo Yurait, Moskva, 2017 , 375 pp.
11. V. A. Baikov, A. V. Zhiber, Uravneniya matematicheskoi fiziki, uchebnik i praktikum dlya akademicheskogo bakalavriata, 2-e izd., Izdatelstvo Yurait, Moskva, 2017 , 255 pp. https://www.biblio-online.ru/book/E4CC7C7D-F3F0-4CD2-8080-579C7F19DA97
12. A. V. Abanin, S. N. Askhabov, A. B. Borisov, R. A. Bostanov, A. V. Zhiber, V. E. Zakharov, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, S. S. Kutateladze, A. V. Mikhailov, A. P. Soldatov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Aleksei Borisovich Shabat (on the occasion of his 80th anniversary)”, Vladikavkaz. Mat. Zh., 19:3 (2017), 83–85  mathnet

   2016
13. A. V. Zhiber, S. N. Kamaeva, “Construction of exact solution to sine-Gordon equation on the base of its characteristic Lie ring”, Ufa Math. Journal, 8:3 (2016), 49–57  mathnet  crossref  mathscinet  isi  elib  elib  scopus
14. A. V. Zhiber, O. S. Kostrigina, “Kharakteristicheskie koltsa Li i simmetrii differentsialnykh uravnenii Penleve I i Penleve III”, Vestnik Bashkirsk. un-ta, 21:3 (2016), 566-574  mathscinet
15. A. V. Zhiber, D. R. Toshmurodova, “Vysshie simmetrii giperbolicheskoi sistemy uravnenii, porozhdennoi uravneniem Penleve IV”, MATEMATIChESKOE MODELIROVANIE PROTsESSOV I SISTEM: Materialy V Vseros. nauch.-prakt. konf., priurochennoi k 110-letiyu so dnya rozhdeniya akademika A.N. Tikhonova, Ch. II. (17-19 noyabrya 2016g., g. Sterlitamak.), eds. S.A. Mustafina, IITs Sterlitamakskogo filiala BashGU, 2016, 215–219
16. N. M. Tsirelman, A. V. Zhiber, Analiticheskoe opredelenie temperaturnykh polei v prostranstvenno-neodnorodnoi i nelineinoi srede, Innovatsionnoe mashinostroenie, Moskva, 2016 , 286 pp.

   2013
17. Yu. G. Voronova, A. V. Zhiber, “Symmetries and Goursat problem for system of equations $u_{xy}=e^{u+v}u_y$, $v_{xy}=-e^{u+v}v_y$”, Ufa Math. Journal, 5:3 (2013), 20–27  mathnet  crossref  mathscinet  elib

   2012
18. Mariya N. Kuznetsova, Asli Pekcan, Anatoliy V. Zhiber, “The Klein–Gordon Equation and Differential Substitutions of the Form $v=\varphi(u,u_x,u_y)$”, SIGMA, 8 (2012), 90 , 37 pp., arXiv: 1111.7255  mathnet (cited: 5)  crossref  mathscinet  isi (cited: 4)  scopus (cited: 5)
19. A. V. Zhiber, R. D. Murtazina, I. T. Habibullin, A. B. Shabat, “Characteristic Lie rings and integrable models in mathematical physics”, Ufimsk. Mat. Zh., 4:3 (2012), 17–85  mathnet  mathscinet  elib
20. M. Gürses, A. V. Zhiber, I. T. Habibullin, “Characteristic Lie rings of differential equations”, Ufimsk. Mat. Zh., 4:1 (2012), 53–62  mathnet  elib
21. A. V. Abanin, S. N. Askhabov, A. B. Borisov, R. A. Bostanov, A. V. Zhiber, V. E. Zakharov, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, S. S. Kutateladze, A. V. Mikhailov, A. P. Soldatov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Shabat Aleksei Borisovich (on his 75th birthday)”, Vladikavkaz. Mat. Zh., 14:2 (2012), 71–73  mathnet  elib

   2011
22. A. V. Zhiber, O. S. Kostrigina, “Goursat problem for nonlinear hyperbolic systems with integrals of the first and second order”, Ufimsk. Mat. Zh., 3:3 (2011), 67–79  mathnet  zmath  elib

   2010
23. Anatoly V. Zhiber, Olga S. Kostrigina, “Characteristic algebras of nonlinear hyperbolic systems of equations”, J. Sib. Fed. Univ. Math. Phys., 3:2 (2010), 173–184  mathnet

   2009
24. A. V. Zhiber, Yu. G. Mihaylova, “Algorithm of building the solution of hyperbolic system of equation”, Ufimsk. Mat. Zh., 1:3 (2009), 28–45  mathnet  zmath  elib

   2008
25. A. V. Zhiber, Yu. G. Mikhailova, “On hyperbolic systems of equations with zero generalized Laplace invariants”, Proc. Steklov Inst. Math. (Suppl.), 261, suppl. 1 (2008), S154–S164  mathnet  crossref  elib  scopus
26. A. V. Zhiber, R. D. Murtazina, “On the characteristic Lie algebras for equations $u_{xy}=f(u,u_x)$”, J. Math. Sci., 151:4 (2008), 3112–3122  mathnet  crossref  mathscinet  zmath  elib (cited: 4)  elib (cited: 4)  scopus (cited: 10)

   2006
27. G. T. Bulgakova, T. A. Faizullin, A. V. Zhiber, “Non-equilibrium two phase filtration”, Matem. Mod., 18:10 (2006), 19–38  mathnet  mathscinet  zmath  elib

   2004
28. A. M. Gurieva, A. V. Zhiber, “Laplace Invariants of Two-Dimensional Open Toda Lattices”, Theoret. and Math. Phys., 138:3 (2004), 338–355  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 11)  elib (cited: 18)

   2003
29. A. V. Zhiber, S. Ya. Startsev, “Integrals, Solutions, and Existence Problems for Laplace Transformations of Linear Hyperbolic Systems”, Math. Notes, 74:6 (2003), 803–811  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 15)  elib (cited: 21)

   2001
30. A. V. Zhiber, V. V. Sokolov, “Exactly integrable hyperbolic equations of Liouville type”, Russian Math. Surveys, 56:1 (2001), 61–101  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 104)  elib (cited: 100)  scopus (cited: 71)

   1999
31. A. V. Zhiber, V. V. Sokolov, “New example of a nonlinear hyperbolic equation possessing integrals”, Theoret. and Math. Phys., 120:1 (1999), 834–839  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 4)  elib (cited: 4)

   1995
32. A. V. Zhiber, “Quasilinear hyperbolic equations with an infinite-dimensional symmetry algebra”, Russian Acad. Sci. Izv. Math., 45:1 (1995), 33–54  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 11)

   1984
33. A. V. Zhiber, A. B. Shabat, “Systems of equations $u_x=p(u, v)$, $v_y=q(u, v)$ that possess symmetries”, Dokl. Akad. Nauk SSSR, 277:1 (1984), 29–33  mathnet  mathscinet  zmath

   1982
34. A. V. Zhiber, “Systems of equations of $n$-waves and nonlinear Schrödinger equations from the group-theoretical point of view”, Theoret. and Math. Phys., 52:3 (1982), 882–888  mathnet  crossref  mathscinet  zmath  isi

   1979
35. A. V. Zhiber, A. B. Shabat, “The Klein–Gordon equation with nontrivial group”, Dokl. Akad. Nauk SSSR, 247:5 (1979), 1103–1107  mathnet  mathscinet
36. A. V. Zhiber, N. H. Ibragimov, A. B. Shabat, “Equations of Liouville type”, Dokl. Akad. Nauk SSSR, 249:1 (1979), 26–29  mathnet  mathscinet  zmath

   1977
37. A. V. Zhiber, “Conservation laws for the equation $u_{tt}-u_{xx}+\sin u=0$”, Funct. Anal. Appl., 11:1 (1977), 55–57  mathnet  crossref  mathscinet  zmath

   1970
38. A. V. Zhiber, A. B. Shabat, Differ. Uravn., 6:1 (1970), 137–146  mathnet  mathscinet  zmath

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