This treatise analyzes the coupled nonlinear system of the model for the ion sound and Langmuir waves. The modified -expansion procedure is utilized to raise new closed-form wave solutions. Those solutions are investigated through hyperbolic, trigonometric and rational function. The graphical design makes the dynamics of the equations noticeable. It provides the mathematical foundation in diverse sectors of underwater acoustics, electromagnetic wave propagation, design of specific optoelectronic devices and physics quantum mechanics. Herein, we concluded that the studied approach is advanced, meaningful and significant in implementing many solutions of several nonlinear partial differential equations occurring in applied sciences.

本论文分析了离子声和朗缪尔波的耦合非线性系统模型。修改后的扩展程序用于提出新的闭合形式的波动解。通过双曲，三角函数和有理函数研究了这些解决方案。图形设计使方程的动态性引人注目。它为水下声学，电磁波传播，特定光电设备的设计以及物理量子力学等各个领域提供了数学基础。在此，我们得出结论，所研究的方法在实施应用科学中出现的几个非线性偏微分方程的许多解决方案方面是先进的，有意义的并且有意义的。