论文标题
非线性随机Manakov系统的Lie-Trotter分裂
Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System
论文作者
论文摘要
本文分析了随机Manakov方程的Lie-Trotter分裂方案的收敛性，这是在随机双折射光纤脉冲传播研究中产生的系统。首先，我们证明，如果系统中的非线性项是全球lipschitz，则数值近似的强度为1/2。然后，我们表明，分裂方案的概率为1/2，几乎可以确定1/2-在立方非线性的情况下。我们提供了几个数字实验，以说明上述结果和lie拖分裂方案的效率。最后，我们从数值上研究了某些幂律非线性的解决方案的可能爆炸。
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.
