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Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System

André Berg 1 David Cohen 2 Guillaume Dujardin 3
3 Paradyse
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
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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https://hal.inria.fr/hal-02975684
Contributor : Guillaume Dujardin Connect in order to contact the contributor
Submitted on : Tuesday, October 27, 2020 - 6:51:44 PM
Last modification on : Tuesday, August 3, 2021 - 4:56:40 PM
Long-term archiving on: : Thursday, January 28, 2021 - 6:03:10 PM

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

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