Linearisation and potential symmetries of certain systems of diffusion equations

C. Sophocleous and R.J. Wiltshire

Physica A: Statistical Mechanics and its Applications, 2006, vol. 370, issue 2, 329-345

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.

Keywords: Systems of diffusion equations; Potential symmetries; Linearising mappings (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:370:y:2006:i:2:p:329-345

DOI: 10.1016/j.physa.2006.03.003

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