Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System
Journal article, 2021

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.

Convergence rates

Almost sure convergence

Coupled system of stochastic nonlinear Schrodinger equations

Lie-Trotter scheme

Stochastic Manakov equation

Strong convergence

Splitting scheme

Stochastic partial differential equations

Convergence in probability


Numerical schemes


Andre Berg

Umeå University

David Cohen

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Guillaume Dujardin

University of Lille

Journal of Scientific Computing

0885-7474 (ISSN) 1573-7691 (eISSN)

Vol. 88 1 6

Numerical analysis and simulation of PDEs with random dispersion

Swedish Research Council (VR) (2018-04443), 2019-01-01 -- 2022-12-31.

Subject Categories

Computational Mathematics

Control Engineering

Mathematical Analysis



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6/7/2021 1