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Exponential integrators for nonlinear Schrödinger equations with white noise dispersion

David Cohen 1 Guillaume Dujardin 2
2 MEPHYSTO - Quantitative methods for stochastic models in physics
Inria Lille - Nord Europe, ULB - Université libre de 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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https://hal.inria.fr/hal-01403036
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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 US, 2017, pp.592-613. ⟨10.1007/s40072-017-0098-1⟩. ⟨hal-01403036⟩

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