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.
Complete list of metadatas

Cited literature [25 references]  Display  Hide  Download

https://hal.inria.fr/hal-01403036
Contributor : Guillaume Dujardin <>
Submitted on : Friday, November 25, 2016 - 2:04:22 PM
Last modification on : Tuesday, July 3, 2018 - 11:29:07 AM
Long-term archiving on : Tuesday, March 21, 2017 - 1:07:00 PM

File

schrodCohenDujardin.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01403036, version 1

Collections

Citation

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⟩

Share

Metrics

Record views

298

Files downloads

266