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Zhiber, Anatoly Vasilievich

Total publications: 33 (29)
in MathSciNet: 19 (19)
in zbMATH: 13 (13)
in Web of Science: 8 (8)
in Scopus: 6 (6)
Cited articles: 18
Citations in Math-Net.Ru: 289
Citations in Web of Science: 128
Citations in Scopus: 81

Number of views:
This page:2462
Abstract pages:7615
Full texts:2614
References:630
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:
| by years | by types | by times cited in WoS | by times cited in Scopus | scientific publications | common list |



   2019
1. 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

   2018
2. 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

   2019
3. 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  scopus

   2017
4. 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
5. 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.
6. 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
7. 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
8. 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  scopus
9. 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
10. 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
11. N. M. Tsirelman, A. V. Zhiber, Analiticheskoe opredelenie temperaturnykh polei v prostranstvenno-neodnorodnoi i nelineinoi srede, Innovatsionnoe mashinostroenie, Moskva, 2016 , 286 pp.

   2013
12. 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
13. 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: 4)  crossref  mathscinet  isi (cited: 4)  scopus (cited: 3)
14. 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
15. M. Gürses, A. V. Zhiber, I. T. Habibullin, “Characteristic Lie rings of differential equations”, Ufimsk. Mat. Zh., 4:1 (2012), 53–62  mathnet
16. 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

   2011
17. 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

   2010
18. 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
19. 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
20. 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
21. 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: 9)

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

   2004
23. 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: 9)  elib (cited: 18)

   2003
24. 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: 13)  elib (cited: 21)

   2001
25. 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: 87)  elib (cited: 100)  scopus (cited: 69)

   1999
26. 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
27. 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
28. 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
29. 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
30. A. V. Zhiber, A. B. Shabat, “The Klein–Gordon equation with nontrivial group”, Dokl. Akad. Nauk SSSR, 247:5 (1979), 1103–1107  mathnet  mathscinet
31. 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
32. 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
33. A. V. Zhiber, A. B. Shabat, Differ. Uravn., 6:1 (1970), 137–146  mathnet  mathscinet  zmath

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