Abstract:

The article deals with the studying of the interaction of gravity waves 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 stepness of the waves, but to be nonintegrable in the next, fifth, order. The exact formula for the five-wave scattering matrix element is obtained using diagram technique on the resonant surface. The stationary solutions of the five-wave kinetic equation are studied as well.