Physical interpretation of exact soliton solutions in the nonlinear Jaulent-Miodek hierarchy equation

Hossain, Md Alamgir; Alam, Md. Nur; Hossain, Md. Farhad; Islam, Md. Ariful; Hassan, Mohammad; Tunç, Cemil

doi:10.22034/cmde.2025.65322.2996

Physical interpretation of exact soliton solutions in the nonlinear Jaulent-Miodek hierarchy equation

Document Type : Research Paper

Authors

¹ Department of Mathematics, Govt. Edward College, Pabna-6600, Bangladesh.

² 1. School of Mathematical Sciences, Sunway University, Bandar Sunway, Petaling Jaya 47500, Selangor Darul Ehsan, Malaysia. 2. Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh. 3. Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamilnadu, India.

³ Department of Mathematics, Pabna University of Science and Technology, Pabna-6600, Bangladesh.

⁴ General Education Department, City University, Khagan, Birulia, Savar, Dhaka-1340, Bangladesh.

⁵ Department of Mathematics and Scientific Computing, Madan Mohan Malaviya University of Technology, Gorakhpur, U.P. India 273010.

⁶ Department of Civil Engineering, School of Engineering and Natural Sciences, Istanbul Medipol University, 34810, Istanbul, Turkey.

10.22034/cmde.2025.65322.2996

Abstract

This study looks at what exact soliton solutions (ESSs) mean in the nonlinear Jaulent-Miodek Hierarchy (NLJMH) equation, which is important because of its energy-related Schr¨odinger potential and its uses in areas like optics, physics, soliton theory, geophysics, fluid dynamics, signal processing, plasma physics, and condensed matter physics. Solitons, as fundamental nonlinear wave structures, play a crucial role in understanding the dynamic behavior of complex systems that are governed by the NLJMH equation. Through rigorous mathematical analysis and symbolic computation techniques, we uncover a range of ESSs, including periodic traveling waves, bright and dark solitons, kink solitons, and their combinations. Each soliton type manifests distinct physical characteristics and behaviors, influencing various phenomena in nonlinear sciences and beyond. Our investigation focuses on elucidating the underlying physical significance of these soliton solutions. By analyzing their profiles, velocities, and interactions, we aim to provide insights into how these nonlinear waves propagate, interact, and impact physical structures. This research contributes to advancing the theoretical comprehension of soliton dynamics within the NLJMH equation framework, highlighting their relevance in fields such as fluid dynamics, plasma physics, optical fibers, and other areas where nonlinear wave phenomena are prevalent. The systematic application of advanced computational tools and rigorous analytical techniques has proven instrumental in uncovering a diverse spectrum of soliton solutions within the NLJMH equation. These findings underscore the method’s effectiveness in generating precise and comprehensive insights into complex nonlinear phenomena. The ability to accurately predict and analyze various soliton types, including kink solitons, periodic traveling waves, bright and dark solitons, and their hybrids, showcases the method’s robustness and versatility. Based on this study, we can conclude that the process used is highly effective, dependable, productive, and potent for resolving any other nonlinear evolution equations (NLEEs).

Keywords

Main Subjects

Theoretical approximation in context of PDEs

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