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<p>Nonlinear wave propagation in fluids is important in modelling various physical phenomena like tsunamis, tidal waves, and ion-acoustic waves. This is commonly done using the nonlinear modified Benjamin-Bona-Mahony (NLMBBM) equation, although a variety of exact analytical solutions that can capture its dynamical characteristics, particularly bifurcations, quasi-periodicity, and chaos, are still rare in the literature. The current solutions will generate a small range of variability of responses, and this restricts our ability to study the complicated wave effects under a realistic setting. To address this gap, the present study suggests a systematic process based on the Modified Extended Tanh Function (METF) approach to produce and analyze a large and diverse space of precise solutions, such as multi-solitons, singular solitons, V-shaped solitons, peakons, periodic, and quasi-periodic, to name a few. Phase-plane analysis, stability, bifurcation analysis, and external periodic perturbation are also used to further analyze the solutions and reveal quasi-periodic and chaotic behaviour. The largest Lyapunov exponent (LLE ≈ 0.08166 &gt; 0) supports the quantitative characterization of chaos. This paper has shown how the METF method is more flexible and superior to the current method of generating a more plentiful solution repertoire. The outputs have better predictive modelling instruments for scientists and engineers in fluid dynamics, coastal engineering, oceanography, plasma physics, and optics, which enhance safer design, better prediction of extreme events, and consistent simulation of complex nonlinear phenomena.</p>

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Bifurcation, Quasi-Periodic, and Chaotic Dynamics in a Nonlinear Fluid Model: Exact Soliton Solutions via Modified Extended Tanh Method

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月29日

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  • Md. Nur Alam,
  • Md Nurul Islam,
  • Shams Forruque Ahmed,
  • Mitiku Daba Firdi,
  • Irfan Anjum Badruddin,
  • Syed Javed

摘要

Nonlinear wave propagation in fluids is important in modelling various physical phenomena like tsunamis, tidal waves, and ion-acoustic waves. This is commonly done using the nonlinear modified Benjamin-Bona-Mahony (NLMBBM) equation, although a variety of exact analytical solutions that can capture its dynamical characteristics, particularly bifurcations, quasi-periodicity, and chaos, are still rare in the literature. The current solutions will generate a small range of variability of responses, and this restricts our ability to study the complicated wave effects under a realistic setting. To address this gap, the present study suggests a systematic process based on the Modified Extended Tanh Function (METF) approach to produce and analyze a large and diverse space of precise solutions, such as multi-solitons, singular solitons, V-shaped solitons, peakons, periodic, and quasi-periodic, to name a few. Phase-plane analysis, stability, bifurcation analysis, and external periodic perturbation are also used to further analyze the solutions and reveal quasi-periodic and chaotic behaviour. The largest Lyapunov exponent (LLE ≈ 0.08166 > 0) supports the quantitative characterization of chaos. This paper has shown how the METF method is more flexible and superior to the current method of generating a more plentiful solution repertoire. The outputs have better predictive modelling instruments for scientists and engineers in fluid dynamics, coastal engineering, oceanography, plasma physics, and optics, which enhance safer design, better prediction of extreme events, and consistent simulation of complex nonlinear phenomena.