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
Blowup
Numerical schemes
Author
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 6Numerical 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
DOI
10.1007/s10915-021-01514-y