Reductions and symmetries for a generalized Fisher equation with a diffusion term dependent on density and space

Abstract

In this work, a generalized Fisher equation with a space–density diffusion term is analyzed by applying the theory of symmetry reductions for partial differential equations. The study of this equation is relevant in terms of its applicability in cell dynamics and tumor invasion. Therefore, classical Lie symmetries admitted by the equation are determined. In addition, by using the multipliers method, we derive some nontrivial conservation laws for this equation. Finally we obtain a direct reduction of order of the ordinary differential equations associated and a particular solution.