Existence of~a~countable set of~integrals of~the motion for a~system of~three three-dimensional wave packets with resonance interaction
Teoretičeskaâ i matematičeskaâ fizika, Tome 44 (1980) no. 2, pp. 224-228
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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.
@article{TMF_1980_44_2_a7,
author = {E. I. Shulman},
title = {Existence of~a~countable set of~integrals of~the motion for a~system of~three three-dimensional wave packets with resonance interaction},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {224--228},
publisher = {mathdoc},
volume = {44},
number = {2},
year = {1980},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1980_44_2_a7/}
}
TY - JOUR AU - E. I. Shulman TI - Existence of~a~countable set of~integrals of~the motion for a~system of~three three-dimensional wave packets with resonance interaction JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1980 SP - 224 EP - 228 VL - 44 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1980_44_2_a7/ LA - ru ID - TMF_1980_44_2_a7 ER -
%0 Journal Article %A E. I. Shulman %T Existence of~a~countable set of~integrals of~the motion for a~system of~three three-dimensional wave packets with resonance interaction %J Teoretičeskaâ i matematičeskaâ fizika %D 1980 %P 224-228 %V 44 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1980_44_2_a7/ %G ru %F TMF_1980_44_2_a7
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. Teoretičeskaâ i matematičeskaâ fizika, Tome 44 (1980) no. 2, pp. 224-228. http://geodesic.mathdoc.fr/item/TMF_1980_44_2_a7/