
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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