Nonclassical symmetry solutions for reaction–diffusion equations with explicit spatial dependence |
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| Authors: | B.H. Bradshaw-Hajek M.P. Edwards P. Broadbridge G.H. Williams |
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| Affiliation: | 1. School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia;2. Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, USA |
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| Abstract: | 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. |
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| Keywords: | Reaction&ndash diffusion equation Nonlinear source Nonclassical symmetry analysis Exact solutions |
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