White noise in the two-dimensional nonlinear schrödinger equation

Abstract

Multiplicative Gaussian white noise is included in the two-dimensional nonlinear Schrödinger equation. The collective coordinate method is used to derive an effective stochastic equation for the width of the wave function. From this equation the coherence time of the ground state solitary wave solution, t_coh , is found to be proportional to D^-1/3 (D is the variance of the noise). Direct numerical simulations indicate t_cohαD^-0.4