Symmetries, Lie and non-Lie exact solutions of  nonlinear reaction-diffusion systems with variable diffusivities

Abstract:
This talk is partly devoted to the classical Lie symmetry analysis of a class of systems of two quasilinear reaction-diffusion equations having variable diffusivities. Moreover, non-Lie reduction to systems of  first order ordinary differential equations is performed for a subclass of these systems. In particular, a wide range of   exact solutions for a degenerate diffusive Lotka-Volterra system are constructed.