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Arrigo, D.J., Broadbridge, P. and Hill, J.M. (1994) Nonclassical Symmetry Reductions of the Linear Diffusion Equation with a Nonlinear Source. Journal of Applied Mathematics, 52, 1-24. http://dx.doi.org/10.1093/imamat/52.1.1

has been cited by the following article:

• TITLE: Group-Invariant Solutions for the Generalised Fisher Type Equation

  AUTHORS: Kirsten Louw, Raseelo J. Moitsheki

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

  JOURNAL NAME: Natural Science, Vol.7 No.13, December 30, 2015

  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.