Exploring accurate soliton propagation in physical systems: a computational study of the (1+1)-dimensional $\mathbb {MNW}$ integrable equation

Abstract

This study investigates the integrable Mikhailov–Novikov–Wang ($\mathbb {MNW}$) equation in (1+1)-dimensional space–time, utilizing rigorous analytical methodologies including the Unified ($\mathbb{U}\mathbb{F}$) and Khater II (${\mathbb {K}}\text {hat.II}$) methods, alongside numerical solutions. Situated within the established mathematical framework of physics, the $\mathbb {MNW}$ equation holds significant relevance in elucidating various physical phenomena, encompassing solitons, nonlinear wave propagation, quantum mechanics, and field theories, contingent upon the specific context and parameters selected for analysis. The primary objective of this study is to conduct a comprehensive analysis of the $\mathbb {MNW}$ equation and propose effective resolution techniques. This is achieved through the amalgamation of diverse analytical and numerical methodologies, facilitating an in-depth exploration of the equation’s characteristics. Noteworthy findings indicate that the $\mathbb{U}\mathbb{F},\, {\mathbb {K}}\text {hat.II}$ methods, in conjunction with He’s variational iteration method, yield robust and highly accurate solutions. The significance of these results lies in their potential to address complex nonlinear equations, providing researchers and practitioners with versatile tools for analysis and interpretation. This research contributes a novel perspective by skillfully integrating these analytical methodologies, thereby advancing the field of mathematical physics and nonlinear differential equations. It is imperative to note that this study is purely theoretical in nature and does not involve specific subjects or participants. The approach adopted is grounded in meticulous numerical experimentation and analytical scrutiny, ensuring rigor and reliability in the findings presented.