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# Exponential integrators for the stochastic Manakov equation

LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : This article presents and analyses an exponential integrator for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optical fibers. We first prove that the strong order of the numerical approximation is $1/2$ if the nonlinear term in the system is globally Lipschitz-continuous. Then, we use this fact to prove that the exponential integrator has convergence order $1/2$ in probability and almost sure order $1/2$, in the case of the cubic nonlinear coupling which is relevant in optical fibers. Finally, we present several numerical experiments in order to support our theoretical findings and to illustrate the efficiency of the exponential integrator as well as a modified version of it.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/hal-02586778
Contributor : Guillaume Dujardin Connect in order to contact the contributor
Submitted on : Friday, May 15, 2020 - 11:35:44 AM
Last modification on : Wednesday, March 23, 2022 - 3:51:28 PM

### Identifiers

• HAL Id : hal-02586778, version 1
• ARXIV : 2005.04978

### Citation

André Berg, David Cohen, Guillaume Dujardin. Exponential integrators for the stochastic Manakov equation. 2020. ⟨hal-02586778⟩

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