Abstract:
A system of equations generated by an operator relation analogous to the Lax operator representation of the Korteweg–de Vries equation is considered. It is shown that the system of equations obtained in this way possesses several infinite series of conservation laws. Conditions for the existence and uniqueness of an analytic solution of the system are found. Consideration is given to the case of an arbitrary number of space variables.
Bibliography: 4 titles.
\Bibitem{Mel79}
\by V.~K.~Mel'nikov
\paper On equations generated by an operator relation
\jour Math. USSR-Sb.
\yr 1980
\vol 36
\issue 3
\pages 351--363
\mathnet{http://mi.mathnet.ru/eng/sm2313}
\crossref{https://doi.org/10.1070/SM1980v036n03ABEH001821}
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\zmath{https://zbmath.org/?q=an:0431.35050|0408.35081}
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Linking options:
https://www.mathnet.ru/eng/sm2313
https://doi.org/10.1070/SM1980v036n03ABEH001821
https://www.mathnet.ru/eng/sm/v150/i3/p378
This publication is cited in the following 9 articles:
V.K. Mel’nikov, “On equations solvable by the inverse scattering method for the Dirac operator”, Communications in Nonlinear Science and Numerical Simulation, 8:1 (2003), 9
D. Fofana, “An integrable system extending the Korteweg–de Vries equation”, Math. USSR-Izv., 39:3 (1992), 1239–1250
O. I. Bogoyavlenskii, “Algebraic constructions of integrable dynamical systems-extensions of the Volterra system”, Russian Math. Surveys, 46:3 (1991), 1–64
O. I. Bogoyavlenskii, “Breaking solitons in $2+1$-dimensional integrable equations”, Russian Math. Surveys, 45:4 (1990), 1–86
O. I. Bogoyavlenskii, “Breaking solitons. III”, Math. USSR-Izv., 36:1 (1991), 129–137
O. I. Bogoyavlenskii, “Some constructions of integrable dynamical systems”, Math. USSR-Izv., 31:1 (1988), 47–75
V. K. Mel'nikov, “Some new nonlinear evolution equations integrable by the inverse problem method”, Math. USSR-Sb., 49:2 (1984), 461–489
Melnikov V., “Symmetries and Conservation-Laws of Dynamical-Systems”, 970, 1982, 146–172
V. K. Mel'nikov, “Conservation laws for a class of systems of nonlinear evolution equations”, Funct. Anal. Appl., 15:1 (1981), 33–47
Citation in format AMSBIB
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