Abstract
| Nonlinear reaction-diffusion equations are used to describe many different
processes in biology and chemistry, for example, population dynamics, cell
proliferation, and chemical reactions. In this talk, I'll show how the
nonclassical symmetry method can be used to find analytic solutions to nonlinear
reaction-diffusion equations. Provided the nonlinear reaction and nonlinear
diffusion terms are related in a certain way, there exists a nonclassical
symmetry that gives rise to a transformation that will linearise and separate
(in time and space) the reaction-diffusion equation, so that analytic solutions
may be constructed. The transformation is valid in different coordinate systems
(eg Cartesian, polar, spherical) and so may be applied in many situations. |