Nonclassical symmetry reductions of the linear diffusion equation with a nonlinear source

Nonclassical symmetry methods are used to study the linear diffusion equation with a nonlinear source term. Mathematical forms are obtained for the source terms which permit a nonclassical symmetry reduction. In addition to the known source terms obtainable from classical symmetry methods, new source terms are found which also admit symmetry reductions. A number of examples are considered and several new exact solutions are constructed, some of which are illustrated graphically. 1