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<p>In this study, we investigate the nonlinear Kakutani–Matsuuchi (NKM) model, which effectively captures the evolution of long internal gravity waves in a stratified fluid medium. Internal gravity waves propagate through fluids with depth-dependent density variations, such as the ocean or atmosphere, and have significant applications in oceanography, plasma physics, fluid dynamics, and related scientific fields. To analyze the NKM model, we employ the trial equation method (TEM), a flexible and robust technique that allows us to obtain exact solutions such as bright solitons, dark solitons, Jacobi elliptic solutions (JES), kinks, and breathers. Additionally, we perform a comprehensive analysis involving phase portraits, equilibrium points, and quasi-periodic behavior, where the system exhibits regular motion at two or more incommensurate frequencies–resulting in predictable but non-repeating dynamics that lie between purely periodic and chaotic behavior. Finally, we conduct a sensitivity analysis to examine how changes in input parameters influence the model’s output, thereby identifying the factors that most significantly affect the system’s response and enhancing the understanding of its stability and predictability.</p>

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Generation of grey and straddled soliton along with chaotic behaviour and sensitivity analysis for internal gravity waves model

  • 期刊论文

  • 发表日期：

    2025年8月8日

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  • Lotfi Jlali,
  • Syed T. R. Rizvi,
  • Asmavia Shahid,
  • Syed K. Naqvi,
  • Atef F. Hashem,
  • Aly R. Seadawy

摘要

In this study, we investigate the nonlinear Kakutani–Matsuuchi (NKM) model, which effectively captures the evolution of long internal gravity waves in a stratified fluid medium. Internal gravity waves propagate through fluids with depth-dependent density variations, such as the ocean or atmosphere, and have significant applications in oceanography, plasma physics, fluid dynamics, and related scientific fields. To analyze the NKM model, we employ the trial equation method (TEM), a flexible and robust technique that allows us to obtain exact solutions such as bright solitons, dark solitons, Jacobi elliptic solutions (JES), kinks, and breathers. Additionally, we perform a comprehensive analysis involving phase portraits, equilibrium points, and quasi-periodic behavior, where the system exhibits regular motion at two or more incommensurate frequencies–resulting in predictable but non-repeating dynamics that lie between purely periodic and chaotic behavior. Finally, we conduct a sensitivity analysis to examine how changes in input parameters influence the model’s output, thereby identifying the factors that most significantly affect the system’s response and enhancing the understanding of its stability and predictability.