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 TMF, 1985, Volume 63, Number 1, Pages 50–63 (Mi tmf4745)

Symmetries and soliton solutions of nonlinear equations

A. N. Leznov, V. I. Man'ko, S. M. Chumakov

Abstract: A new, purely algebraic method is developed for finding soliton solutions of nonlinear equations; it does not require the use of the formalism of the inverse scattering method. As examples, explicit expressions for soliton solutions are constructed for some wellknown equations as well as some not hitherto discussed in the literature. The symmetry basis of the method is associated with infinite-dimensional Lie algebras, these being internal symmetry algebras of the systems considered.

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English version:
Theoretical and Mathematical Physics, 1985, 63:1, 356–365

Bibliographic databases:

Citation: A. N. Leznov, V. I. Man'ko, S. M. Chumakov, “Symmetries and soliton solutions of nonlinear equations”, TMF, 63:1 (1985), 50–63; Theoret. and Math. Phys., 63:1 (1985), 356–365

Citation in format AMSBIB
\Bibitem{LezManChu85} \by A.~N.~Leznov, V.~I.~Man'ko, S.~M.~Chumakov \paper Symmetries and soliton solutions of nonlinear equations \jour TMF \yr 1985 \vol 63 \issue 1 \pages 50--63 \mathnet{http://mi.mathnet.ru/tmf4745} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=794471} \zmath{https://zbmath.org/?q=an:0584.35006} \transl \jour Theoret. and Math. Phys. \yr 1985 \vol 63 \issue 1 \pages 356--365 \crossref{https://doi.org/10.1007/BF01017835} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1985ATJ6000004}