Classification of coupled systems with two-component nonlinear diffusion equations by the invariant subspace method

The invariant subspace method is developed to perform classification of systems with two-component nonlinear diffusion equations, which was carried out with respect to the invariant subspaces Wn11xWn22 defined by linear ordinary differential equations. As a result, the corresponding exact solutions generated by invariant subspaces to the resulting systems are obtained. In most cases, two components of these exact solutions belong to different 'scalar' subspaces. Behaviour to several exact solutions of the systems is described.