An attempt at a numerical solution of the potential wave equations

The primitive equations for nonlinear potential waves are solved using the pseudo-courier method. This allows conservation of 4 integrai invaiaants. The initial conditions are assumed to be superposition of the waves satisfying the dispersive relation. 'The amplitudes corresponded to the Phillips spectrum. The main results are as follows. Nonlinearity is revealed very distinctly in the loss of determinate relation between wave numbers and frequency, which manifests itself in the phase velocity variation in time. The RMS deviation grovus with increasing frequency. The mean frequency of all waves is systematically greater than the Stokes-wave frequency. Increasing nonlineari-ty results in independence of wave velocity of the wave number. This effect has been found earlier in laboratory experiments.