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Journal Articles Journal of Scientific Computing Year : 2021

Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System

Abstract

This article analyses the convergence of the Lie-Trotter splitting scheme for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optical fibers. First, we prove that the strong order of the numerical approximation is 1/2 if the nonlinear term in the system is globally Lipschitz. Then, we show that the splitting scheme has convergence order 1/2 in probability and almost sure order 1/2- in the case of a cubic nonlinearity. We provide several numerical experiments illustrating the aforementioned results and the efficiency of the Lie-Trotter splitting scheme. Finally, we numerically investigate the possible blowup of solutions for some power-law nonlinearities.
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Dates and versions

hal-02975684 , version 1 (27-10-2020)

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André Berg, David Cohen, Guillaume Dujardin. Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System. Journal of Scientific Computing, 2021, 88 (6), ⟨10.1007/s10915-021-01514-y⟩. ⟨hal-02975684⟩
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