Numerical and computational investigation of soliton propagation in physical systems via computational schemes: (1+1)-dimensional [formula omitted] integrable equation

Abstract

This study utilizes computational and numerical techniques to investigate the (1+1)-dimensional Mikhailov–Novikov–Wang (MNW) integrable equation, a nonlinear partial differential equation that governs the propagation of solitons in various physical systems, including plasma physics and fluid dynamics. The numerical methods proposed in this research provide an accurate and efficient means of obtaining wave solutions for the MNW equation. Through the application of these techniques, new soliton solutions are derived, expressed in terms of hyperbolic and trigonometric functions, and analyzed to determine their amplitude and shape characteristics. The results obtained demonstrate the potential of the proposed numerical methods to solve other nonlinear partial differential equations in fields such as engineering and physics. The findings of this study have significant implications for understanding the dynamics of solitons in physical systems and may facilitate the development of more effective numerical methods for solving nonlinear partial differential equations.