Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 162, Issue 3-4, Pages 131-154Publisher
ELSEVIER
DOI: 10.1016/S0167-2789(01)00379-7
Keywords
nonlinear Schrodinger equation; blow-up phenomena; finite-difference methods; white noise
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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.
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