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Teoreticheskaya i Matematicheskaya Fizika, 1980, Volume 44, Number 2, Pages 224–228 (Mi tmf3498)  
Existence of a countable set of integrals of the motion for a system of three three-dimensional wave packets with resonance interaction

E. I. Shulman
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Abstract: It is shown that three-dimensional form of three-wave interaction for bounded envelopes, possesses an infinite sequence of conservation laws. Recurrent relation which enables one to obtain conservation laws of arbitrary order $N$ is presented. In contrast to the one-dimensional case the conservation laws are nonpolynomial for $N\geqslant3$ and include essentially nonlocal terms.
Received: 15.05.1979
English version:
Theoretical and Mathematical Physics, 1980, Volume 44, Issue 2, Pages 708–710
DOI: https://doi.org/10.1007/BF01018451
Bibliographic databases:
Language: Russian
Citation: E. I. Shulman, “Existence of a countable set of integrals of the motion for a system of three three-dimensional wave packets with resonance interaction”, TMF, 44:2 (1980), 224–228; Theoret. and Math. Phys., 44:2 (1980), 708–710
Citation in format AMSBIB
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\by E.~I.~Shulman
\paper Existence of~a~countable set of~integrals of~the motion for a~system of~three three-dimensional wave packets with resonance interaction
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\yr 1980
\vol 44
\issue 2
\pages 224--228
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=587303}
\transl
\jour Theoret. and Math. Phys.
\yr 1980
\vol 44
\issue 2
\pages 708--710
\crossref{https://doi.org/10.1007/BF01018451}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980LL99100008}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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