Exact and traveling-wave solutions for convection–diffusion–reaction equation with power-law nonlinearity

Abstract

Based on the simplest equation method, we propose exact and traveling-wave solutions for a nonlinear convection–diffusion–reaction equation with power law nonlinearity. Such equation can be considered as a generalization of the Fisher equation and other well-known convection–diffusion–reaction equations. Two important cases are considered. The case of density-independent diffusion and the case of density-dependent diffusion. When the parameters of the equation are constant, the Bernoulli equation is used as the simplest equation. This leads to new traveling-wave solutions. Moreover, some wavefront solutions can be derived from the traveling-wave ones. The case of time-dependent velocity in the convection term is studied also. We derive exact solutions of the equations by using the Riccati equation as simplest equation. The exact and traveling-wave solutions presented in this paper can be used to explain many biological and physical phenomena.