New structures for closed-form wave solutions for the dynamical equations model related to the ion sound and Langmuir waves
Md. Nur Alam, M.S. Osman
Abstract
Abstract This treatise analyzes the coupled nonlinear system of the model for the ion sound and Langmuir waves. The modified <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>G</mml:mi> <mml:mo accent="false">′</mml:mo> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>G</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> -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.