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.
Dr Yuri V Lvov