The investigation into the exact solutions of the generalized time-delayed Burgers–Fisher equation with positive fractional power terms

The time-delayed Burgers–Fisher equation is very important model to forest fire, population growth, Neolithic transitions, the interaction between the reaction mechanism, convection effect and diffusion transport, etc. In this paper, the solitary wave solutions of the generalized time-delayed Burgers–Fisher equation with positive fractional power terms are derived with the aid of a subsidiary high-order ODE, and the solitary wave solutions of the special type of generalized time-delayed Burgers–Fisher equation are presented. From the expressions of the solitary wave solutions, it is easy to obtain how the time-delayed constant τ works upon soliton velocity and width of the soliton, and these exact solutions are very important to understand the physical mechanism of the phenomena described by the time-delayed Burgers–Fisher equation.