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<p>This study investigates the Chafee–Infante (CI) equation, a nonlinear partial differential equation widely used in the modeling of reaction–diffusion systems. The CI equation plays a pivotal role in understanding wave propagation and stability phenomena in systems characterized by nonlinear reactions and diffusion effects. Despite its importance, the equation has not yet been explored using the sub-equation method. In this work, we apply the sub-equation method as an effective analytical tool to derive novel exact traveling wave solutions to the CI equation. The obtained solutions include anti-peakon solitons, stumpons, periodic waves with anti-peaked crests and troughs, and kink-type solitons. These distinct wave structures are visualized through 2D and 3D surface plots, contour diagrams, and density profiles by selecting appropriate parameter values, thereby confirming the theoretical predictions. The significance of this study lies in introducing a new analytical perspective for solving the CI equation and expanding the known solution space. The results demonstrate the robustness and versatility of the sub-equation method in capturing complex nonlinear behaviors. Furthermore, the findings contribute to a deeper understanding of nonlinear wave dynamics, with potential applications in gas diffusion, thermal processes, and other systems affected by nonlinear instabilities and temperature driven dynamics.</p>

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Advanced modeling and visualizations of the Chafee–Infante equation in reaction–diffusion systems

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Saman Naz,
  • Umair Asghar,
  • Muhammad Imran Asjad,
  • M. S. Alqarni

摘要

This study investigates the Chafee–Infante (CI) equation, a nonlinear partial differential equation widely used in the modeling of reaction–diffusion systems. The CI equation plays a pivotal role in understanding wave propagation and stability phenomena in systems characterized by nonlinear reactions and diffusion effects. Despite its importance, the equation has not yet been explored using the sub-equation method. In this work, we apply the sub-equation method as an effective analytical tool to derive novel exact traveling wave solutions to the CI equation. The obtained solutions include anti-peakon solitons, stumpons, periodic waves with anti-peaked crests and troughs, and kink-type solitons. These distinct wave structures are visualized through 2D and 3D surface plots, contour diagrams, and density profiles by selecting appropriate parameter values, thereby confirming the theoretical predictions. The significance of this study lies in introducing a new analytical perspective for solving the CI equation and expanding the known solution space. The results demonstrate the robustness and versatility of the sub-equation method in capturing complex nonlinear behaviors. Furthermore, the findings contribute to a deeper understanding of nonlinear wave dynamics, with potential applications in gas diffusion, thermal processes, and other systems affected by nonlinear instabilities and temperature driven dynamics.