|
This article is cited in 6 scientific papers (total in 6 papers)
New example of a nonlinear hyperbolic equation possessing integrals
A. V. Zhibera, V. V. Sokolovb
a Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences
b Landau Institute for Theoretical Physics, Centre for Non-linear Studies
Abstract:
We discover an important new case in the classical problem of the classification of nonlinear hyperbolic equations possessing integrals. In the general (least degenerate) case, in addition, we obtain a formula describing the splitting of the right-hand side of such equations with respect to the first derivatives.
DOI:
https://doi.org/10.4213/tmf757
 Full text:
PDF file (172 kB)
References:
PDF file
HTML file
English version:
Theoretical and Mathematical Physics, 1999, 120:1, 834–839
Bibliographic databases:
   
Received: 30.10.1998
Revised: 19.11.1998
Citation:
A. V. Zhiber, V. V. Sokolov, “New example of a nonlinear hyperbolic equation possessing integrals”, TMF, 120:1 (1999), 20–26; Theoret. and Math. Phys., 120:1 (1999), 834–839
Citation in format AMSBIB
\Bibitem{ZhiSok99}
\by A.~V.~Zhiber, V.~V.~Sokolov
\paper New example of a nonlinear hyperbolic equation possessing integrals
\jour TMF
\yr 1999
\vol 120
\issue 1
\pages 20--26
\mathnet{http://mi.mathnet.ru/tmf757}
\crossref{https://doi.org/10.4213/tmf757}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1737201}
\zmath{https://zbmath.org/?q=an:0957.35092}
\elib{https://elibrary.ru/item.asp?id=13311983}
\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 120
\issue 1
\pages 834--839
\crossref{https://doi.org/10.1007/BF02557393}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000083293900002}
Linking options:
http://mi.mathnet.ru/eng/tmf757https://doi.org/10.4213/tmf757 http://mi.mathnet.ru/eng/tmf/v120/i1/p20
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
V. E. Adler, A. B. Shabat, R. I. Yamilov, “Symmetry approach to the integrability problem”, Theoret. and Math. Phys., 125:3 (2000), 1603–1661
 -
A. V. Zhiber, V. V. Sokolov, “Exactly integrable hyperbolic equations of Liouville type”, Russian Math. Surveys, 56:1 (2001), 61–101
 -
M. Pobořil, “A new hyperbolic equation possessing a zero-curvature representation”, J. Math. Sci., 136:6 (2006), 4484–4485
-
D. K. Demskoi, “One Class of Liouville-Type Systems”, Theoret. and Math. Phys., 141:2 (2004), 1509–1527
-
Skrypnyk, T, “Integrable deformations of the mKdV and SG hierarchies and quasigraded Lie algebras”, Physica D-Nonlinear Phenomena, 216:2 (2006), 247
 -
Gubbiotti G. Yamilov R.I., “Darboux Integrability of Trapezoidal H-4 and H-4 Families of Lattice Equations i: First Integrals”, J. Phys. A-Math. Theor., 50:34 (2017), 345205, 1–26
|
| Number of views: |
| This page: | 452 | | Full text: | 210 | | References: | 25 | | First page: | 1 |
|
Terms of Use