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<p>This investigation explores long-wavelength disturbance propagation in fluid dynamics and plasma physics under weak nonlinearity and dispersion. The principal aim is to develop computational solutions using the Khater III (Khat III) and modified Kudryashov (MKud) techniques. For solution validation, He’s variational iteration (HVI) method is implemented, thereby ensuring solution robustness. Numerical comparisons demonstrate strong agreement between the derived analytical solutions and computational simulations, thereby validating the model’s descriptive power for nonlinear wave phenomena. Additionally, a systematic bifurcation analysis of the nonlinear Typical Kadomtsev Petviashvili (TKP)model identifies equilibrium states, analyzes transitions between chaotic and quasi-periodic regimes, and evaluates the associated planar dynamical system’s sensitivity. Through implementation of sophisticated analytical methodologies, this work advances comprehension of nonlinear evolution equations and their applications, providing valuable insights for applied mathematics, fluid dynamics, and plasma physics. The established theoretical foundation supports future investigations into nonlinear wave propagation across diverse physical systems.</p>

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Precision in wave propagation and bifurcation analysis: advanced symbolic techniques for nonlinear dynamics in fluid and plasma systems

  • 期刊论文

  • 发表日期：

    2025年5月2日

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  • Mostafa M. A. Khater

摘要

This investigation explores long-wavelength disturbance propagation in fluid dynamics and plasma physics under weak nonlinearity and dispersion. The principal aim is to develop computational solutions using the Khater III (Khat III) and modified Kudryashov (MKud) techniques. For solution validation, He’s variational iteration (HVI) method is implemented, thereby ensuring solution robustness. Numerical comparisons demonstrate strong agreement between the derived analytical solutions and computational simulations, thereby validating the model’s descriptive power for nonlinear wave phenomena. Additionally, a systematic bifurcation analysis of the nonlinear Typical Kadomtsev Petviashvili (TKP)model identifies equilibrium states, analyzes transitions between chaotic and quasi-periodic regimes, and evaluates the associated planar dynamical system’s sensitivity. Through implementation of sophisticated analytical methodologies, this work advances comprehension of nonlinear evolution equations and their applications, providing valuable insights for applied mathematics, fluid dynamics, and plasma physics. The established theoretical foundation supports future investigations into nonlinear wave propagation across diverse physical systems.