ABSTRACT

A numerical solution of the direct scattering problem for the system of Zakharov–Shabat equations is considered. Based on the Marchuk identity, a method of fourth-order approximation accuracy is proposed. A numerical simulation of the scattering problem is made using two characteristic boundary value problems with known solutions as an example. The calculations have shown that the algorithm has high accuracy, which is necessary in many practical applications of optical and acoustic sensing in applied optics and geophysics.

中文翻译：

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Zakharov-Shabat直接散射问题的数值解

摘要

考虑了Zakharov-Shabat方程组直接散射问题的数值解。基于马尔库克恒等式，提出了一种四阶近似精度的方法。使用两个特征边界值问题（以已知解决方案为例）对散射问题进行了数值模拟。计算表明，该算法具有很高的精度，这在应用光学和地球物理学中的光学和声学传感的许多实际应用中是必需的。