Affiliation:
1. School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia
Abstract
This paper considers reaction-diffusion equations from a new point of view, by including spatiotemporal dependence in the source terms. We show for the first time that solutions are given in terms of the classical Painlevé transcendents. We consider reaction-diffusion equations with cubic and quadratic source terms. A new feature of our analysis is that the coefficient functions are also solutions of differential equations, including the Painlevé equations. Special cases arise with elliptic functions as solutions. Additional solutions given in terms of equations that are not integrable are also considered. Solutions are constructed using a Lie symmetry approach.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Analysis
Reference9 articles.
1. Explicit solutions of Fisher's equation for a special wave speed
2. National Bureau of Standards Applied Mathematics Series;Abramowitz M.,1964
3. Applied Mathematical Sciences;Bluman G. W.,2002
4. Nonclassical symmetry solutions for reaction–diffusion equations with explicit spatial dependence
5. Wiley Series in Mathematical and Computational Biology;Cantrell R. S.,2003
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