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 Mat. Sb. (N.S.), 1979, Volume 108(150), Number 3, Pages 378–392 (Mi msb2313)

On equations generated by an operator relation

V. K. Mel'nikov

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.

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English version:
Mathematics of the USSR-Sbornik, 1980, 36:3, 351–363

Bibliographic databases:

UDC: 517.9
MSC: Primary 35K22; Secondary 35Q20

Citation: V. K. Mel'nikov, “On equations generated by an operator relation”, Mat. Sb. (N.S.), 108(150):3 (1979), 378–392; Math. USSR-Sb., 36:3 (1980), 351–363

Citation in format AMSBIB
\Bibitem{Mel79} \by V.~K.~Mel'nikov \paper On equations generated by an operator relation \jour Mat. Sb. (N.S.) \yr 1979 \vol 108(150) \issue 3 \pages 378--392 \mathnet{http://mi.mathnet.ru/msb2313} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=530317} \zmath{https://zbmath.org/?q=an:0431.35050|0408.35081} \transl \jour Math. USSR-Sb. \yr 1980 \vol 36 \issue 3 \pages 351--363 \crossref{https://doi.org/10.1070/SM1980v036n03ABEH001821} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KM96900005} 

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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:
1. V. K. Mel'nikov, “Conservation laws for a class of systems of nonlinear evolution equations”, Funct. Anal. Appl., 15:1 (1981), 33–47
2. Melnikov V., “Symmetries and Conservation-Laws of Dynamical-Systems”, 970, 1982, 146–172
3. V. K. Mel'nikov, “Some new nonlinear evolution equations integrable by the inverse problem method”, Math. USSR-Sb., 49:2 (1984), 461–489
4. O. I. Bogoyavlenskii, “Some constructions of integrable dynamical systems”, Math. USSR-Izv., 31:1 (1988), 47–75
5. O. I. Bogoyavlenskii, “Breaking solitons in $2+1$-dimensional integrable equations”, Russian Math. Surveys, 45:4 (1990), 1–89
6. O. I. Bogoyavlenskii, “Breaking solitons. III”, Math. USSR-Izv., 36:1 (1991), 129–137
7. D. Fofana, “An integrable system extending the Korteweg–de Vries equation”, Math. USSR-Izv., 39:3 (1992), 1239–1250
8. O. I. Bogoyavlenskii, “Algebraic constructions of integrable dynamical systems-extensions of the Volterra system”, Russian Math. Surveys, 46:3 (1991), 1–64
9. 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
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