5-WAVE INTERACTION ON THE SURFACE OF DEEP FLUID

This article deals with the studying of the interaction of gravity wav es propagating on the surface of an ideal fluid of infinite depth. The system of the corresponding equation is proven to be integrable up to the fourth order in power of steepness of the waves, but to be nonint egrable in the next, fifth, order. An exact formula for the five-wave scattering matrix element is obtained using diagram technique on the r esonant surface. The stationary solutions of the five-wave kinetic equ ation are studied as well.