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Mat. Sb. (N.S.), 1983, Volume 121(163), Number 4(8), Pages 469–498 (Mi msb2219)  

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

Some new nonlinear evolution equations integrable by the inverse problem method

V. K. Mel'nikov


Abstract: Several new nonlinear evolution equations integrable by the inverse problem method are obtained. The method applied in finding these equations is believed to be essentially new. The comparison of that method with other methods for finding nonlinear evolution equations integrable by the inverse problem method is given. In particular, it is shown that the methods using the Heisenberg equation (the so-called Lax representation) are not suitable to obtain the equations studied here.
Bibliography: 23 titles.

Full text: PDF file (1403 kB)
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English version:
Mathematics of the USSR-Sbornik, 1984, 49:2, 461–489

Bibliographic databases:

UDC: 517.9
MSC: 35K22, 35K55
Received: 11.03.1982

Citation: V. K. Mel'nikov, “Some new nonlinear evolution equations integrable by the inverse problem method”, Mat. Sb. (N.S.), 121(163):4(8) (1983), 469–498; Math. USSR-Sb., 49:2 (1984), 461–489

Citation in format AMSBIB
\Bibitem{Mel83}
\by V.~K.~Mel'nikov
\paper Some new nonlinear evolution equations integrable by the inverse problem method
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 121(163)
\issue 4(8)
\pages 469--498
\mathnet{http://mi.mathnet.ru/msb2219}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=716108}
\zmath{https://zbmath.org/?q=an:0558.35063}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 49
\issue 2
\pages 461--489
\crossref{https://doi.org/10.1070/SM1984v049n02ABEH002721}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. M. Krichever, “Spectral theory of finite-zone nonstationary Schrödinger operators. A nonstationary Peierls model”, Funct. Anal. Appl., 20:3 (1986), 203–214  mathnet  crossref  mathscinet  zmath  isi
    2. Zakharov V., Kuznetsov E., “Multiscale Expansions in the Theory of Systems Integrable by the Inverse Scattering Transform”, Physica D, 18:1-3 (1986), 455–463  crossref  mathscinet  zmath  adsnasa  isi
    3. N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, “Quantum current lie algebra as the universal algebraic structure of the symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics”, Theoret. and Math. Phys., 75:1 (1988), 329–339  mathnet  crossref  mathscinet  zmath  isi
    4. 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
    5. I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Russian Math. Surveys, 66:1 (2011), 107–144  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Runliang Lin, Xiaojun Liu, Yunbo Zeng, “Bilinear Identities and Hirota's Bilinear Forms for an Extended Kadomtsev-Petviashvili Hierarchy”, Journal of Nonlinear Mathematical Physics, 20:2 (2013), 214  crossref
    7. Adam Doliwa, Runliang Lin, “Discrete KP equation with self-consistent sources”, Physics Letters A, 2014  crossref
    8. Runliang Lin, Xiaojun Liu, Yunbo Zeng, “The KP hierarchy with self–consistent sources: construction, Wronskian solutions and bilinear identities”, J. Phys.: Conf. Ser, 538 (2014), 012014  crossref
    9. Q. Li, J. B. Zhang, D. Y. Chen, “The Eigenfunctions and Exact Solutions of Discrete mKdV Hierarchy with Self-Consistent Sources via the Inverse Scattering Transform”, Adv. Appl. Math. Mech, 7:05 (2015), 663  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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