Nonlinear Dynamics of the Dual-Mode Chaffee-Infante Equation: Solitary Waves, Modulation Instability, and Sensitivity Effects

This work is based on finding dual-mode solitary wave solutions of the dual-mode Chaffee-Infante equation which is a significant model in reaction-diffusion systems and nonlinear dynamics. This model addresses important physical properties such as phase velocity, dispersion, and nonlinearity. A range of solutions, including periodic, singular soliton, bright soliton, and dark soliton, are obtained by the implementation of two reliable and efficient approaches namely: the modified F-expansion method and [Formula: see text] - expansion approach. Two- and three-dimensional graphs are presented for illustrating the behavior of the obtained solutions. The modulation instability analysis confirmed that the governing model is stable under small perturbations. Moreover, the dynamical behavior of the model has been investigated using sensitivity analysis and bifurcation analysis.