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


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, 44:2, 708–710

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