Conditional Lie-Bäcklund Symmetries and Reductions of the Nonlinear Diffusion Equations with Source

Abstract

Conditional Lie-Bäcklund symmetry approach is used to study the invariant subspace of the nonlinear diffusion equations with source $u_t=e^{-qx}{(e^{px}P(u)u_x^m)}_x+Q(x,u)$, $m\ne 1$. We obtain a complete list of canonical forms for such equations admit multidimensional invariant subspaces determined by higher order conditional Lie-Bäcklund symmetries. The resulting equations are either solved exactly or reduced to some finite-dimensional dynamic systems.