aDepartment of Mathematics and Statistics, University of Cyprus, CY 1678 Nicosia, Cyprus
bThe Division of Mathematics and Statistics, The University of Glamorgan, Pontypridd CF37 1DL, UK
Abstract:
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.