On a generalized Fisher equation

A generalized non-linear Fisher equation in cylindrical coordinates with radial symmetry is studied from Lie symmetry point of view. In the classical Fisher equation the reaction diffusion term is replaced with a general function to accommodate more equations of this type. Moreover, the diffusivity is assumed to be a function of the dependent variable to account for many real situations. An attempt is made to classify the diffusivity function and exact solutions are obtained in some cases.

Research highlights
► A generalized non-linear Fisher equation in cylindrical coordinates with radial symmetry is studied using Lie point symmetry point of view.
► In the classical Fisher equation the reaction diffusion term is replaced with a general function to accommodate more equations of this type. Moreover, diffusivity is assumed to be a function of the dependent variable to account for many real situations.
► Exact solutions in some cases of the non-linear Fisher equation are obtained.