Stochastic perturbations of nonlinear dispersive waves

Wave propagation phenomena, in particular self focusing in certain molecular systems subject to thermal fluctuations may be mathematically modeled with the use of systems of discrete equations with random perturbations, which in the continuous limit give rise to stochastic nonlinear dispersive equation, as e.g. the stochastic nonlinear Schrödinger equation. From the point of view of models, we study here the influence of different kinds of stochastic perturbations, which will always be white noise, i.e. δ-correlated in time, on the dynamical behavior of the solutions, as e.g. wave collapse, or soliton propagation. It appears, as a result of theoretical studies as well as numerical computations, on the stochastic models, that the dynamical behavior of the waves strongly depends on the spatial correlations of the noise.