论文标题
随机马纳科夫方程的指数积分器
Exponential integrators for the stochastic Manakov equation
论文作者
论文摘要
本文介绍并分析了随机Manakov方程的指数积分器，这是一种在随机双向光纤维中脉冲传播的研究中产生的系统。我们首先证明，如果系统中的非线性术语在全球lipschitz-continules上，数值近似的强度为$ 1/2 $。然后，我们使用这个事实证明指数积分器的概率为$ 1/2 $，几乎可以肯定的是$ 1/2 $，如果是在光纤中相关的立方非线性耦合。最后，我们提出了几个数值实验，以支持我们的理论发现并说明指数积分器的效率以及它的修改版本。
This article presents and analyses an exponential integrator for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optical fibers. We first prove that the strong order of the numerical approximation is $1/2$ if the nonlinear term in the system is globally Lipschitz-continuous. Then, we use this fact to prove that the exponential integrator has convergence order $1/2$ in probability and almost sure order $1/2$, in the case of the cubic nonlinear coupling which is relevant in optical fibers. Finally, we present several numerical experiments in order to support our theoretical findings and to illustrate the efficiency of the exponential integrator as well as a modified version of it.
