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Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 115, Pages 264–273 (Mi znsl4058)  

This article is cited in 7 scientific papers (total in 8 papers)

Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations

L. A. Takhtadzhyan, L. D. Faddeev
Full-text PDF (402 kB) Citations (8)
Abstract: One gives a simple and general derivation of the well-known connection between the geometric and the Hamiltonian approaches in the classical method of the inverse problem. Namely, for the case of a two-dimensional auxiliary problem and periodic boundary conditions it is explicitly shown how the existence of the classical $r$-matrix for the integrable equations leads to their representation in the form of the condition of zero curvature.
English version:
Journal of Soviet Mathematics, 1985, Volume 28, Issue 5, Pages 800–806
DOI: https://doi.org/10.1007/BF02112346
Bibliographic databases:
Document Type: Article
UDC: 517.93
Language: Russian
Citation: L. A. Takhtadzhyan, L. D. Faddeev, “Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Zap. Nauchn. Sem. LOMI, 115, "Nauka", Leningrad. Otdel., Leningrad, 1982, 264–273; J. Soviet Math., 28:5 (1985), 800–806
Citation in format AMSBIB
\Bibitem{TakFad82}
\by L.~A.~Takhtadzhyan, L.~D.~Faddeev
\paper Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~14
\serial Zap. Nauchn. Sem. LOMI
\yr 1982
\vol 115
\pages 264--273
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl4058}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=660088}
\zmath{https://zbmath.org/?q=an:0562.35088|0505.35082}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 28
\issue 5
\pages 800--806
\crossref{https://doi.org/10.1007/BF02112346}
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  • https://www.mathnet.ru/eng/znsl/v115/p264
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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