Linearisation and potential symmetries of certain systems of diffusion equations
Wiltshire, R. J.
SourcePhysica A: Statistical Mechanics and its Applications
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We consider systems of two pure one-dimensional diffusion equations that have considerable interest in Soil Science and Mathematical Biology. We construct non-local symmetries for these systems. These are determined by expressing the equations in a partially and wholly conserved form, and then by performing a potential symmetry analysis on those systems that can be linearised. We give several examples of such systems, and in a specific case we show how linearising and hodograph-type mappings can lead to new solutions of the diffusion system. © 2006 Elsevier B.V. All rights reserved.