Abstract:
The paper is devoted to group-theoretical analysis of a system of equations of n-waves and a system of nonlinear Schrödinger equations. The Lie–Bäcklund algebras of these equations are fully described. These algebras are commutative, and there is a one-toone correspondence between them and the commutative Lie algebras of the conservation laws. The connection between the Lie–Bäcklund algebras of the considered systems of equations is found.
Citation:
A. V. Zhiber, “Systems of equations of n-waves and nonlinear Schrödinger equations from the group-theoretical point of view”, TMF, 52:3 (1982), 405–413; Theoret. and Math. Phys., 52:3 (1982), 882–888
\Bibitem{Zhi82}
\by A.~V.~Zhiber
\paper Systems of equations of $n$-waves and nonlinear Schr\"odinger equations from the group-theoretical point of view
\jour TMF
\yr 1982
\vol 52
\issue 3
\pages 405--413
\mathnet{http://mi.mathnet.ru/tmf2565}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=692932}
\zmath{https://zbmath.org/?q=an:0505.35074}
\transl
\jour Theoret. and Math. Phys.
\yr 1982
\vol 52
\issue 3
\pages 882--888
\crossref{https://doi.org/10.1007/BF01038083}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1982QL36200007}
Linking options:
https://www.mathnet.ru/eng/tmf2565
https://www.mathnet.ru/eng/tmf/v52/i3/p405
This publication is cited in the following 2 articles:
A. V. Kiselev, “Methods of geometry of differential equations in analysis of integrable models of field theory”, J. Math. Sci., 136:6 (2006), 4295–4377
S. S. Titov, “Solution of nonlinear equations in analytic polyalgebras. I”, Russian Math. (Iz. VUZ), 44:1 (2000), 65–75
Citation in format AMSBIB
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