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

• Published in: Computational & applied mathematics Vol. 43; no. 3
• Main Author: Khater, Mostafa M. A.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Iterative methods; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Nonlinear differential equations; Nonlinear equations; Numerical methods; Quantum mechanics; Robustness (mathematics); Solitary waves; Wave propagation; He’s variational iteration method; Unified method; Khater II method; 65M06; 35Q53; Integrable equation; 37K10; 35C08
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-024-02639-0

This study investigates the integrable Mikhailov–Novikov–Wang ( MNW ) equation in (1+1)-dimensional space–time, utilizing rigorous analytical methodologies including the Unified ( U F ) and Khater II ( K hat.II ) methods, alongside numerical solutions. Situated within the established mathematical framework of physics, the 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 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 U F , K 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.