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Conditional Lie–Bäcklund Symmetries and Invariant Subspaces to Nonlinear Diffusion Equations with Convection and Source


Address for correspondence: Changzheng Qu, Center for Nonlinear Studies, Ningbo University, Ningbo 315211, P.R. China; e-mail:


The conditional Lie–Bäcklund 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–Bäcklund 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.

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