Numerical simulations of focusing stochastic nonlinear Schrodinger equations

In this paper, we numerically investigate nonlinear Schrodinger equations with a stochastic contribution which is of white noise type and acts either as a potential (multiplicative noise) or as a forcing term (additive noise). In the subcritical case, we recover similar results as in the case of the Korteweg-de Vries equation. In the critical or supercritical case, we observe that depending on its smoothness, the noise may have different effects. Spatially smooth noises amplify blow-up phenomena, whereas delta correlated multiplicative noises prevent blow-up formation. Note that in this latter case, very few results are known, both from a theoretical and a numerical point of view. (C) 2002 Elsevier Science B.V. All rights reserved.