Conditional Lie-B?cklund symmetries and invariant subspaces to nonlinear diffusion equations with convection and source

摘要

The conditional Lie-B?cklund symmetry method is used to study the invariant subspace of the nonlinear diffusion equations with convection and source terms. We obtain a complete list of canonical forms for such equations which admit higher order conditional Lie-B?cklund symmetries and multidimensional invariant subspaces. The functionally generalized separable solutions to the resulting equations are constructed due to the corresponding symmetry reductions. For most of the cases, they are reduced to solving finite-dimensional dynamical systems.