A STOCHASTIC APPROACH TO THE THEORY OF NONLINEAR-WAVE TRAINS NEAR MARGINAL STABILITY

By employing the turbulent theoretical approach of Alber [1], Davidson [5] and Roy and Bhakta [8] the dynamical evolution of the wave spectr um of nonlinear wavetrains near marginal stability is derived starting from a derivative nonlinear Schrodinger equation, extended with a qui ntic nonlinearity, called the EDNLS-equation. The stability of three h omogeneous background spectral densities (the delta-, the normal- and the uniform distribution), is investigated in the linear regime. The m ost important findings in that respect as as follows: First, the delta -distribution instability criterion deviates by a numerical factor fro m the one presented in Fla and Wyller [6] for the modulational instabi lity in the EDNLS-equation. Secondly, the growth rate of this instabil ity result in the limit of small, but finite spectral width limit is e quivalent with the turbulence theory result based on the derivative no nlinear Schrodinger equation up to module translation in the central w ave number.