Abstract

We give a complete description of one-dimensional 4-wave resonance interactions in which some extra quantities (besides momentum, energy, number of quasiparticles) are conserved. In this way we obtain new consideration laws for the kinetic equations for waves. In particular, we consider waves in optical fibers, the system of four resonantly interacting wave packets, long wave interactions of annihilation-creation type, various wave systems with quadratic dispersion laws. The results can be important for various problems concerning nonlinear wave dynamics, e.g. for nonlinear optics of waveguides.

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