Conditional Lie–Bäcklund Symmetries and Functionally Generalized Separation of Variables to Quasi-Linear Diffusion Equations with Source

Abstract

The conditional Lie–Bäcklund symmetry method is applied to investigate the functionally generalized separation of variables for quasi-linear diffusion equations with a source. The equations and the admitted conditional Lie–Bäcklund symmetries related to invariant subspaces are identified. The exact solutions possessing the form of the functionally generalized separation of variables are constructed for the resulting equations due to the corresponding symmetry reductions.