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.
Cite
@article{arxiv.2010.15679,
title = {Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System},
author = {André Berg and David Cohen and Guillaume Dujardin},
journal= {arXiv preprint arXiv:2010.15679},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:2005.04978