Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 004, 11 pages      nlin.SI/0601036      https://doi.org/10.3842/SIGMA.2006.004

On Linearizing Systems of Diffusion Equations

Christodoulos Sophocleous a and Ron J. Wiltshire b
a) Department of Mathematics and Statistics, University of Cyprus, CY 1678 Nicosia, Cyprus
b) The Division of Mathematics and Statistics, The University of Glamorgan, Pontypridd CF37 1DL, Great Britain

Received November 23, 2005, in final form January 10, 2006; Published online January 16, 2006

Abstract
We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence transformations of the second generation potential system to derive forms of this system that can be linearized. In turn, these transformations lead to nonlocal mappings that linearize the original system.

Key words: diffusion equations; equivalence transformations; linearization.

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