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 $${{\frac{1}{2}-}}$$ 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.