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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.

KEYWORDS

Symmetry Methods, Modified Hopf-Cole Transformation, Fisher Type Equation, Exact Solutions

Cite this paper

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.





Author: Kirsten Louw, Raseelo J. Moitsheki

Source: http://www.scirp.org/



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