The Method of Linear Determining Equations to Evolution System and Application for Reaction-Diffusion System with Power Diffusivities

The method of linear determining equations is constructed to study conditional Lie–Backlund symmetry and the differential constraint of a two-component second-order evolution system, which generalize the determining equations used in the search for classical Lie symmetry. As an application of the approach, the two-component reaction-diffusion system with power diffusivities is considered. The conditional Lie–Backlund symmetries and differential constraints admitted by the reaction-diffusion system are identified. Consequently, the reductions of the resulting system are established due to the compatibility of the corresponding invariant surface conditions and the original system.