Nonlinear evolution of the spectrum of swell

It is shown that the general four-wave kinetic equation for the spectrum of swell can be greatly simplified owing to spectrum narrowness. A dimensiona l analysis of the equations of the directional approximation makes it possi ble to write them in a self-similar form and to obtain analytical power-law time dependences for the main parameters of the swell spectrum-frequency o f a spectral peak omega(m), wave energy e, and others. It is also shown tha t the corresponding self-similar system of equations describing the nonline ar evolution of the swell spectrum has an analytical solution, which determ ines a self-similar form of the swell spectrum.