Exponential integrators for nonlinear Schrödinger equations with white noise dispersion

David Cohen 1 Guillaume Dujardin 2, 3
3 MEPHYSTO - Quantitative methods for stochastic models in physics
Inria Lille - Nord Europe, ULB - Université Libre de Bruxelles [Bruxelles], LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : This article deals with the numerical integration in time of the nonlinear Schrödinger equation with power law nonlinearity and random dispersion. We introduce a new explicit exponential integrator for this purpose that integrates the noisy part of the equation exactly. We prove that this scheme is of mean-square order 1 and we draw consequences of this fact. We compare our exponential integrator with several other numerical methods from the literature. We finally propose a second exponential integrator, which is implicit and symmetric and, in contrast to the first one, preserves the $L 2-norm$ of the solution.
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Stochastics and Partial Differential Equations Analysis and Computations, Springer, 2017
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David Cohen, Guillaume Dujardin. Exponential integrators for nonlinear Schrödinger equations with white noise dispersion. Stochastics and Partial Differential Equations Analysis and Computations, Springer, 2017. 〈hal-01403036〉

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