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

This article is cited in 9 scientific papers (total in 9 papers)

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
Received: 06.04.1978

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
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\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
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\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  mathnet  crossref  mathscinet  zmath  isi
    2. Melnikov V., “Symmetries and Conservation-Laws of Dynamical-Systems”, 970, 1982, 146–172  mathscinet  isi
    3. V. K. Mel'nikov, “Some new nonlinear evolution equations integrable by the inverse problem method”, Math. USSR-Sb., 49:2 (1984), 461–489  mathnet  crossref  mathscinet  zmath
    4. O. I. Bogoyavlenskii, “Some constructions of integrable dynamical systems”, Math. USSR-Izv., 31:1 (1988), 47–75  mathnet  crossref  mathscinet  zmath
    5. O. I. Bogoyavlenskii, “Breaking solitons in $2+1$-dimensional integrable equations”, Russian Math. Surveys, 45:4 (1990), 1–89  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. O. I. Bogoyavlenskii, “Breaking solitons. III”, Math. USSR-Izv., 36:1 (1991), 129–137  mathnet  crossref  mathscinet  zmath  adsnasa
    7. D. Fofana, “An integrable system extending the Korteweg–de Vries equation”, Math. USSR-Izv., 39:3 (1992), 1239–1250  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. O. I. Bogoyavlenskii, “Algebraic constructions of integrable dynamical systems-extensions of the Volterra system”, Russian Math. Surveys, 46:3 (1991), 1–64  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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