Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System

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.

Automated summary

This article analyzes the convergence of the Lie-Trotter splitting scheme for the stochastic Manakov equation, proving that the strong order of the numerical approximation is 1/2 under globally Lipschitz nonlinear conditions. It demonstrates that the splitting scheme has a convergence order of 1/2 in probability and almost sure order 1/2- for cubic nonlinearities. Numerical experiments illustrate the results and efficiency of the scheme, while also investigating potential blowup of solutions for certain power-law nonlinearities.