Nonclassical symmetry solutions for reaction-diffusion equations with explicit spatial dependence

摘要

Nonclassical symmetry methods are used to study the linear diffusion equation with a nonlinear source term which includes explicit spatial dependence. Mathematical forms for the spatial dependence are found which enable strictly nonclassical symmetries to be admitted when the nonlinearity is cubic. A number of new exact solutions are constructed, and an application of one of these solutions to diploid population genetics is discussed. (C) 2006 Elsevier Ltd. All rights reserved.