Diffusion and degradation effect switching closed form solitons to a nonlinear mathematical model

This study investigates the (2+1)-dimensional Chaffee-Infante equation, an important nonlinear model in gravitation, fluid dynamics, and the Poincaré conjecture with diffusion and degradation coefficients. Using the improved Bernoulli sub-equation function (IBSEF) method, we extract new soliton solutions, including kink, breather, and periodic waves depending on the diffusion coefficient α and degradation coefficient λ in terms of hyperbolic and exponential functions and their combinations. We analyze these solutions using phase plane and bifurcation analyses to understand their dynamic behavior and stability. We identify different equilibrium points, such as saddle point, center, and focus, and examine their stability. Using Matlab, we depict graphs to show how α and λ affect wave patterns and stability. This gives us a better understanding of the system’s dynamics. The results demonstrate that the IBSEF method is efficient and reliable, assisting us to investigate new and stable soliton solutions to complex nonlinear equations in mathematical physics and engineering. This research contributes significantly to understanding nonlinear wave phenomena and their applications in various scientific fields.