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<p>Solitary wave propagation is vital structure in nonlinear science due to their stability and persistence. In this work, we explore the diverse soliton solutions and quasi-periodic structures for the Sharma–Tasso–Olver–Burgers equation. By applying the generalized Arnous method and the new modified generalized exponential rational function method, we obtain bright solitons, dark solitons, periodic waves, singular structures, and exponential-type localized solutions. The formation and propagation of these waves are captured through graphical illustration of 3D, 2D and density plots and validity of results confirmed. Additionally, we perturb the dynamical system corresponding to the studied equation and observe quasi-periodic behavior in the perturbed system using various chaos detection tools. These results have potential applications in fluid dynamics, plasma physics, nonlinear optics, and high-speed signal transmission.</p>

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Analyzing soliton wave structures and chaotic dynamics for the Sharma–Tasso–Olver–Burgers equation: theoretical analysis and simulations

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • Jan Muhammad,
  • Usman Younas,
  • Muhammad Naveed Rafiq,
  • Muhammad Hamza Rafiq

摘要

Solitary wave propagation is vital structure in nonlinear science due to their stability and persistence. In this work, we explore the diverse soliton solutions and quasi-periodic structures for the Sharma–Tasso–Olver–Burgers equation. By applying the generalized Arnous method and the new modified generalized exponential rational function method, we obtain bright solitons, dark solitons, periodic waves, singular structures, and exponential-type localized solutions. The formation and propagation of these waves are captured through graphical illustration of 3D, 2D and density plots and validity of results confirmed. Additionally, we perturb the dynamical system corresponding to the studied equation and observe quasi-periodic behavior in the perturbed system using various chaos detection tools. These results have potential applications in fluid dynamics, plasma physics, nonlinear optics, and high-speed signal transmission.