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Linearisation and potential symmetries of certain systems of diffusion equations

Author

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  • Sophocleous, C.
  • Wiltshire, R.J.

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.

Suggested Citation

  • Sophocleous, C. & Wiltshire, R.J., 2006. "Linearisation and potential symmetries of certain systems of diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 329-345.
    • Handle: RePEc:eee:phsmap:v:370:y:2006:i:2:p:329-345
    DOI: 10.1016/j.physa.2006.03.003
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