Classical and potential symmetries for a generalized Fisher equation

Abstract

In this work, we consider a generalized Fisher equation and we have considered this equation from the point of view of the theory of symmetry reductions in partial differential equations. Generalizations of the Fisher equation are needed to more accurately model complex diffusion and reaction effects found in many biological systems. The reductions to ordinary differential equations are derived from the optimal system of subalgebras and new exact solutions are obtained. The potential system has been achieved from the complete list of the conservation laws. Potential symmetries, which are not local symmetries, are carried out for the generalized Fisher equation, these symmetries lead to the linearization of the equation by non-invertible mappings.