Chaotic behavior and solution structures of the Chaffee–Infante equation under external forces

This study presents the dynamical analysis and soliton solutions of the Chaffee–Infante equation, an important nonlinear evolution model. The Chaffee Infante equation, widely employed as a reaction–diffusion model, is used to characterize mass transport and particle diffusion in various scientific domains. Applications of this equation span fluid dynamics, electromagnetic wave fields, high-energy physics, fluid mechanics, coastal engineering, ion-acoustic waves in plasma physics, and optical fibers. The considered equation is transformed into an ordinary differential equation using Lie symmetries, which is further utilized to find analytical solutions through the sub equation technique. To study how wave solutions change with parameter variations, we produced 2D and 3D visualizations, as well as contour plots in Mathematica, and used them to compare solution behavior across parameter sets. The detailed study of the mentioned equation is carried out and includes the analysis of bifurcation at fixed points in the system and chaotic behavior in the system in presence of an external force based on 3D and 2D plots, the contour plots, phase portraits, multi-stability analysis, Poincaré maps, Lyapunov exponents, and time series analysis. The models sensitivity to varying initial conditions is also analyzed.