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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
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English version:
Theoretical and Mathematical Physics, 1999, 120:1, 834–839
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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
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http://mi.mathnet.ru/eng/tmf757https://doi.org/10.4213/tmf757 http://mi.mathnet.ru/eng/tmf/v120/i1/p20
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V. E. Adler, A. B. Shabat, R. I. Yamilov, “Symmetry approach to the integrability problem”, Theoret. and Math. Phys., 125:3 (2000), 1603–1661
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A. V. Zhiber, V. V. Sokolov, “Exactly integrable hyperbolic equations of Liouville type”, Russian Math. Surveys, 56:1 (2001), 61–101
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M. Pobořil, “A new hyperbolic equation possessing a zero-curvature representation”, J. Math. Sci., 136:6 (2006), 4484–4485
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D. K. Demskoi, “One Class of Liouville-Type Systems”, Theoret. and Math. Phys., 141:2 (2004), 1509–1527
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Skrypnyk, T, “Integrable deformations of the mKdV and SG hierarchies and quasigraded Lie algebras”, Physica D-Nonlinear Phenomena, 216:2 (2006), 247
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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
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