Document Type : Research Paper
Authors
1
Department of Mathematics, Govt. Edward College, Pabna-6600, Bangladesh.
2
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 Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, Van, Turkey.
Abstract
This experiment delves into the physical interpretation of exact soliton solutions (ESSs) in the nonlinear Jaulent Miodek Hierarchy (JMH) equation. Solitons, as fundamental nonlinear wave structures, performance a crucial role in understanding the dynamic behavior of complex systems are governed by the JMH equation. Through rigorous mathematical analysis and symbolic computation techniques, we uncover a range of exact soliton solutions, 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 comprehending of soliton dynamics within the JMH 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 nonlinear Jaulent Miodek Hierarchy (JMH) 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.
Keywords
Main Subjects
)