Nonclassical Symmetry Solutions for Non-Autonomous Reaction-Diffusion Equations

Abstract

The behaviour of many systems in chemistry, combustion and biology can be described using nonlinear reaction diffusion equations. Here, we use nonclassical symmetry techniques to analyse a class of nonlinear reaction diffusion equations, where both the diffusion coefficient and the coefficient of the reaction term are spatially dependent. We construct new exact group invariant solutions for several forms of the spatial dependence, and the relevance of some of the solutions to population dynamics modelling is discussed.

Keywords

• nonclassical symmetries
• Q-conditional symmetries
• Lie symmetries
• exact solutions
• reaction-diffusion equations
• spatially-dependent diffusion
• population dynamics