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<p>In this article, we employ two advanced analytical techniques, the Modified Khater method (MKhat) and Nucci’s direct reduction technique to analyze the Konopelchenko–Dubrovsky equations for the first time. These methods yield novel analytical solutions, previously unexplored in the literature, for a class of integrable systems highly valuable for theoretical and mathematical investigations. Our study generates several new soliton solutions, including those involving trigonometric, periodic, exponential, and elliptic functions, as well as unique forms such as periodic solutions, cusped decay solitary solutions, stumpon solutions, peakon solutions, and kink-type solutions. The innovative application of these techniques not only simplifies the resolution of integrable systems but also provides efficient approaches for deriving soliton solutions, enhancing our understanding of the Konopelchenko–Dubrovsky equations. The results underscore the importance of exploring diverse wave phenomena across various scientific domains. Applications include ocean engineering, where wave dynamics and interactions in shallow and deep waters are studied; nonlinear optics, particularly in modeling optical solitons in fiber systems with dispersive and nonlinear effects; plasma physics, investigating plasma wave behaviors and charged particle interactions; and condensed matter physics, exploring solitonic structures in crystal lattices and other complex systems. To provide physical insights and better visual understanding, <Emphasis FontCategory="NonProportional">Mathematica</Emphasis> software is used to create graphical representations of the solutions, including 3D, 2D, and contour plots. Additionally, chaos and sensitivity analyses are performed to investigate the dynamic aspects of the governing model, with periodic and quasi-periodic trajectory plots offering a deeper understanding of the system’s behavior. The Konopelchenko–Dubrovsky equations are well-regarded for modeling nonlinear wave phenomena in diverse physical contexts. This study not only highlights the broader significance of the model but also makes a significant contribution to the field, offering impactful results that pave the way for future advancements in related research areas.</p>

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Dynamics of Advanced Soliton Wave Profiles in a Nonlinear Model with Some Structural Behavior: Chaos Theory and Sensitivity Analysis

  • 期刊论文

  • 发表日期：

    2025年7月18日

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  • Umair Asghar,
  • Muhammad Imran Asjad,
  • Sachin Kumar,
  • Suhad Ali Osman Abdallah

摘要

In this article, we employ two advanced analytical techniques, the Modified Khater method (MKhat) and Nucci’s direct reduction technique to analyze the Konopelchenko–Dubrovsky equations for the first time. These methods yield novel analytical solutions, previously unexplored in the literature, for a class of integrable systems highly valuable for theoretical and mathematical investigations. Our study generates several new soliton solutions, including those involving trigonometric, periodic, exponential, and elliptic functions, as well as unique forms such as periodic solutions, cusped decay solitary solutions, stumpon solutions, peakon solutions, and kink-type solutions. The innovative application of these techniques not only simplifies the resolution of integrable systems but also provides efficient approaches for deriving soliton solutions, enhancing our understanding of the Konopelchenko–Dubrovsky equations. The results underscore the importance of exploring diverse wave phenomena across various scientific domains. Applications include ocean engineering, where wave dynamics and interactions in shallow and deep waters are studied; nonlinear optics, particularly in modeling optical solitons in fiber systems with dispersive and nonlinear effects; plasma physics, investigating plasma wave behaviors and charged particle interactions; and condensed matter physics, exploring solitonic structures in crystal lattices and other complex systems. To provide physical insights and better visual understanding, Mathematica software is used to create graphical representations of the solutions, including 3D, 2D, and contour plots. Additionally, chaos and sensitivity analyses are performed to investigate the dynamic aspects of the governing model, with periodic and quasi-periodic trajectory plots offering a deeper understanding of the system’s behavior. The Konopelchenko–Dubrovsky equations are well-regarded for modeling nonlinear wave phenomena in diverse physical contexts. This study not only highlights the broader significance of the model but also makes a significant contribution to the field, offering impactful results that pave the way for future advancements in related research areas.