Non-linear reaction–diffusion systems with variable diffusivities: Lie symmetries, ansätze and exact solutions

This work first considers the classical Lie symmetry analysis of a class of systems of two quasilinear reaction–diffusion equations having variable diffusivities. Subsequently, non-Lie reductions to systems of first order ordinary differential equations are obtained for a subclass of these systems. In particular, families of exact solutions of a diffusive Lotka–Volterra type system are constructed.  2004 Elsevier Inc. All rights reserved