Exact Solitary Wave Profiles for the Fisher Equation with Nonlinear Convection Term Arising in Physical Sciences

In this manuscript, the reaction-diffusion Fisher equation is investigated analytically with the nonlinear convection term. The physical, chemical, and biological sciences all rely on the memory effect in the diffusion reaction equation. We obtained the exact solitary wave profiles of memory effect in the Fisher equation by using the generalized Riccati equation mapping method. After applying this method, we obtained analytical solutions for the memory effect in Fisher equation, like as trigonometric, hyperbolic, rational, and exponential functions. We designed the Three-Dimensional (3D), Two-Dimensional (2D), and their contour for the appropriate values of the parameters by using MATHEMATICA. These solutions provide us with more understanding of the memory effect in the Fisher equation.