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<p>In this study, we focus on deriving solitary wave solutions for a (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili equation, which holds significant importance in fluid mechanics and ocean engineering for modeling the elastic and non-elastic interactions of internal waves. Utilizing the widely recognized new extended direct algebraic method, we obtain a diverse range of innovative optical soliton solutions, including anti-kink, dark, singular, periodic singular, and multiple dark-bright solitons, expressed in rational, hyperbolic, and exponential forms. These solutions are visualized in 3D, 2D, and density plots using <Emphasis FontCategory="NonProportional">Wolfram Mathematica</Emphasis> to elucidate their physical characteristics. Furthermore, a comprehensive sensitivity analysis is conducted to investigate the impact of key parameters on the behavior of the solutions under varying conditions. This study has profound practical applications in fluid mechanics and ocean engineering, where the derived solutions offer vital clues about the behavior of internal waves, including their elastic and non-elastic interactions, which are essential for understanding wave dynamics in stratified fluids, oceanographic phenomena, and energy transfer processes in marine environments.</p>

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Dynamic solitary waves in the (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili equation: exact solutions and sensitivity analysis

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Azad Ali Sagher,
  • Muhammad Imran Asjad,
  • Naeem Ullah,
  • Marei S. Alqarni

摘要

In this study, we focus on deriving solitary wave solutions for a (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili equation, which holds significant importance in fluid mechanics and ocean engineering for modeling the elastic and non-elastic interactions of internal waves. Utilizing the widely recognized new extended direct algebraic method, we obtain a diverse range of innovative optical soliton solutions, including anti-kink, dark, singular, periodic singular, and multiple dark-bright solitons, expressed in rational, hyperbolic, and exponential forms. These solutions are visualized in 3D, 2D, and density plots using Wolfram Mathematica to elucidate their physical characteristics. Furthermore, a comprehensive sensitivity analysis is conducted to investigate the impact of key parameters on the behavior of the solutions under varying conditions. This study has profound practical applications in fluid mechanics and ocean engineering, where the derived solutions offer vital clues about the behavior of internal waves, including their elastic and non-elastic interactions, which are essential for understanding wave dynamics in stratified fluids, oceanographic phenomena, and energy transfer processes in marine environments.