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Exponential integrators for the stochastic Manakov equation

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.
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https://hal.inria.fr/hal-02586778
Contributor : Guillaume Dujardin <>
Submitted on : Friday, May 15, 2020 - 11:35:44 AM
Last modification on : Friday, November 27, 2020 - 2:18:03 PM

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

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

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