Novel Solitary Wave Solutions and Stability Analysis of the Generalized (3+1)-Dimensional Chaffee–Infante Equation

The generalized (3+1)-dimensional Chaffee–Infante equation, a nonlinear evolution equation with dispersive, dissipative and nonlinear effects, is considered a member of the class of reaction–diffusion models. Applying the Khater III method, we obtain seventeen exact analytical solutions of hyperbolic, trigonometric and rational function forms. The accuracy of these solutions is verified by comparison with the numerical simulations obtained by He's variational iteration method. The satisfactory consistency at absolute error levels less than 10^ - 9 supports the reliability of the analytical results. The analysis shows different dynamical patterns: solitary waves, periodic structures and singular wave profiles and studies their stability properties under parameter variation. The results generalize the known solution structure of the Chaffee-Infante framework and provide a mathematical setting to study similar spatiotemporal patterns of nonlinear population dynamics.