Group-Invariant Solutions for the Generalised Fisher Type Equation

DOI: 10.4236/ns.2015.713061   PDF   HTML   XML   4,322 Downloads   4,800 Views   Citations

Abstract

In this paper, we construct the group-invariant (exact) solutions for the generalised Fisher type equation using both classical Lie point and the nonclassical symmetry techniques. The generalised Fisher type equation arises in theory of population dynamics. The diffusion term and coefficient of the source term are given as the power law functions of the spatial variable. We introduce the modified Hopf-Cole transformation to simplify a nonlinear second Order Ordinary Equation (ODE) into a solvable linear third order ODE.

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Louw, K. and Moitsheki, R. (2015) Group-Invariant Solutions for the Generalised Fisher Type Equation. Natural Science, 7, 613-624. doi: 10.4236/ns.2015.713061.

Conflicts of Interest

The authors declare no conflicts of interest.

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