Open Access

ARTICLE

New Soliton Wave Solutions to a Nonlinear Equation Arising in Plasma Physics

by M. B. Almatrafi, Abdulghani Alharbi^*

Department of Mathematics, Faculty of Science, Taibah University, Saudi Arabia

* Corresponding Author: Abdulghani Alharbi. Email:

(This article belongs to the Special Issue: Integration of Geometric Modeling and Numerical Simulation)

Computer Modeling in Engineering & Sciences 2023, 137(1), 827-841. https://doi.org/10.32604/cmes.2023.027344

Received 25 October 2022; Accepted 30 December 2022; Issue published 23 April 2023

Abstract

The extraction of traveling wave solutions for nonlinear evolution equations is a challenge in various mathematics, physics, and engineering disciplines. This article intends to analyze several traveling wave solutions for the modified regularized long-wave (MRLW) equation using several approaches, namely, the generalized algebraic method, the Jacobian elliptic functions technique, and the improved Q-expansion strategy. We successfully obtain analytical solutions consisting of rational, trigonometric, and hyperbolic structures. The adaptive moving mesh technique is applied to approximate the numerical solution of the proposed equation. The adaptive moving mesh method evenly distributes the points on the high error areas. This method perfectly and strongly reduces the error. We compare the constructed exact and numerical results to ensure the reliability and validity of the methods used. To better understand the considered equation’s physical meaning, we present some 2D and 3D figures. The exact and numerical approaches are efficient, powerful, and versatile for establishing novel bright, dark, bell-kink-type, and periodic traveling wave solutions for nonlinear PDEs.

---

Keywords

---