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.

本文分析了随机Manakov方程的Lie-Trotter分裂方案的收敛性，该系统是研究随机双折射光纤中脉冲传播的系统。首先，我们证明，如果系统中的非线性项是全局Lipschitz，则数值逼近的强阶为1/2。然后，我们证明在三次非线性情况下，分裂方案的收敛阶数为1/2，几乎确定阶数为\（{{\ frac {1} {2}-}} \\）。我们提供了几个数值实验，说明了上述结果以及Lie-Trotter分裂方案的效率。最后，我们通过数值研究了某些幂律非线性的解的可能爆破。