  Similarity reductions and new exact solutions are obtained for a nonlinear
diffusion equation. These are obtained by using the classical symmetry group
and reducing the partial differential equation to various ordinary differential
equations. For the equations so obtained, first integrals are deduced which
consequently give rise to explicit solutions. Potential symmetries, which are
realized as local symmetries of a related auxiliary system, are obtained. For
some special nonlinearities new symmetry reductions and exact solutions are
derived by using the nonclassical method.
