NONCLASSICAL SYMMETRIES FOR NONLINEAR DIFFUSION AND ABSORPTION

Nonclassical symmetry methods are used to study the nonlinear diffusio n equation with a nonlinear source, In particular, exponential and pow er law diffusivities are examined and we obtain mathematical forms of the source term which permit nonclassical symmetry reductions, In addi tion to the known source terms obtained by classical symmetry methods, we find new source terms which admit symmetry reductions, We also ded uce a class of nonclassical symmetries which are valid for arbitrary d iffusivity and deduce corresponding new solution types, This is an imp ortant result since previously only traveling wave solutions were know n to exist for arbitrary diffusivity, A number of examples are conside red and new exact solutions are constructed.