In this work, we develop an efficient numerical scheme based on the method of lines (MOL) to investigate the interesting phenomenon of collisions and reflections of optical solitons. The established scheme is of second order in space and of fourth order in time with an explicit nature. We deduce stability restrictions using the von Neumann stability analysis. We consider a \((2+ 1)\)-dimensional system of a coupled nonlinear Schrödinger equation as a general model of nonlinear Schrödinger-type equations. We consider several numerical experiments to demonstrate the robustness of the scheme in capturing many scenarios of collisions and reflections of the optical solitons related to nonlinear Schrödinger-type equations. We verify the scheme accuracy through computing the conserved invariants and comparing the present results with some existing ones in the literature.

在这项工作中，我们开发了一种基于线法 (MOL) 的有效数值方案，以研究光学孤子碰撞和反射的有趣现象。已建立的方案在空间上是二阶的，在时间上是四阶的，具有明确的性质。我们使用冯诺依曼稳定性分析推导出稳定性限制。我们考虑一个\((2+1)\)耦合非线性薛定谔方程的维系统作为非线性薛定谔型方程的一般模型。我们考虑了几个数值实验来证明该方案在捕捉与非线性薛定谔型方程相关的光学孤子的许多碰撞和反射场景方面的鲁棒性。我们通过计算守恒不变量并将当前结果与文献中的一些现有结果进行比较来验证方案的准确性。