Further transformation properties of generalised inhomogeneous nonlinear diffusion equations with variable coefficients

Christodoulos Sophocleous

Physica A: Statistical Mechanics and its Applications, 2005, vol. 345, issue 3, 457-471

Abstract: We consider the variable coefficient inhomogeneous nonlinear diffusion equations of the form xput=[xqunux]x. We present further transformation properties for this nonlinear class of equations that do not appear in the literature. In particular, we map this class of variable-coefficient into constant-coefficient evolution equations. We also introduce hodograph and generalised hodograph transformation. For a specific form of this class we derive an auto-hodograph transformation. New nonlocal symmetries known as potential symmetries are found. Finally, examples of exact solutions are given.

Keywords: Nonlinear diffusion equations; Local and nonlocal symmetries; Form-preserving transformations; Hodograph transformations (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:345:y:2005:i:3:p:457-471

DOI: 10.1016/j.physa.2004.07.018

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