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<p>This study focuses on the Chaffee-Infante equation, a widely used reaction-diffusion model in optical fluid dynamics, electrical field theory, coastal technology and plasma physics. The model effectively describes fundamental mechanisms such as mass transport and particle diffusion. To achieve exact traveling wave solutions, we utilize a novel form of the extended direct algebraic approach. The generated soliton solutions exhibit a wide spectrum of forms, including bell-shaped, combined bright and dark, multiple bright and dark, kink-shaped with flat structure, periodic, and singular wave structures. Graphical simulations conducted in <Emphasis FontCategory="NonProportional">Wolfram Mathematica</Emphasis> demonstrate that parameter variations significantly affect soliton amplitude and velocity. Also perform the dynamical theory in which, Bifurcation analysis reveals clear transitions from stable soliton states to chaotic regimes when the nonlinear parameter exceeds the critical value <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="339_2025_8937_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \approx 0.85\)</EquationSource> </InlineEquation>. Phase portraits confirm these transitions, displaying the evolution from limit cycles to strange attractors. Time-series analysis, based on sinusoidal, cosine, and exponential functions, highlights irregular oscillations in chaotic regions, while sensitivity analysis indicates that even minor perturbations (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="339_2025_8937_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(&lt;2\%\)</EquationSource> </InlineEquation>) in parameter values cause notable shifts in wave profiles. Overall, the suggested method is shown to be a powerful tool for deriving closed-form soliton solutions and for capturing intricate dynamical features of the Chaffee-Infante model.</p>

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Deriving new closed-form solitary waves of nonlinear model occurring in mass transport and particle diffusion and their dynamical behaviors

  • 期刊论文

  • 发表日期：

    2025年9月24日

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  • Muhammad Imran Asjad,
  • Hira Ashiq,
  • Nadia Cheemaa,
  • Umair Asghar,
  • Marei S. Alqarni

摘要

This study focuses on the Chaffee-Infante equation, a widely used reaction-diffusion model in optical fluid dynamics, electrical field theory, coastal technology and plasma physics. The model effectively describes fundamental mechanisms such as mass transport and particle diffusion. To achieve exact traveling wave solutions, we utilize a novel form of the extended direct algebraic approach. The generated soliton solutions exhibit a wide spectrum of forms, including bell-shaped, combined bright and dark, multiple bright and dark, kink-shaped with flat structure, periodic, and singular wave structures. Graphical simulations conducted in Wolfram Mathematica demonstrate that parameter variations significantly affect soliton amplitude and velocity. Also perform the dynamical theory in which, Bifurcation analysis reveals clear transitions from stable soliton states to chaotic regimes when the nonlinear parameter exceeds the critical value \(\alpha \approx 0.85\) . Phase portraits confirm these transitions, displaying the evolution from limit cycles to strange attractors. Time-series analysis, based on sinusoidal, cosine, and exponential functions, highlights irregular oscillations in chaotic regions, while sensitivity analysis indicates that even minor perturbations ( \(<2\%\) ) in parameter values cause notable shifts in wave profiles. Overall, the suggested method is shown to be a powerful tool for deriving closed-form soliton solutions and for capturing intricate dynamical features of the Chaffee-Infante model.