On some explicit solitary wave patterns for a generalized nonlinear reaction–diffusion equation with conformable temporal fractional derivative

Abstract

Soliton solutions of a (2+1)-dimensional reaction–diffusion problem are derived in the present work using the generalized Riccati equation mapping method. The model captures the time evaluation of disturbance and addresses modeling real-world phenomena such as turbulence, traffic flow, heat and fluid transport, and gas dynamics. To start with, the nonlinear conformable time fractional transformation is employed to derive a general nonlinear ordinary differential equation from the nonlinear reaction–diffusion equation. Next, we find exact solutions of this model through the application of the generalized Riccati equation mapping approach. This methodology yields numerous families of solutions, including solitary waves and solitons. We obtain various forms of solutions, including singular, dark, kink, and bright solitons. For illustration purposes, we provide graphs of some exact solutions in the form of three-dimensional plots, two-dimensional plots and contour graphs.

Keywords

• (2 ＋ 1)-dimensional nonlinear reaction–diffusion equation
• Nonlinear fractional evolution equation
• Generalized Riccati equation mapping method