Potential Nonclassical Symmetries and Solutions of Fast Diffusion Equation

Details Potential Nonclassical Symmetries and Solutions of Fast Diffusion Equation Potential Nonclassical Symmetries and Solutions of Fast Diffusion Equation

2005-06-26

arxiv.org/abs/math-ph/0506067v3

Phys. Lett. A 362 (2007) 166-173

Physics

Mathematical Physics

13 pages, section 3 is essentially revised

Scientific paper

10.1016/j.physleta.2006.10.015

The fast diffusion equation $u_t=(u^{-1}u_x)_x$ is investigated from the symmetry point of view in development of the paper by Gandarias [Phys. Lett. A 286 (2001) 153-160]. After studying equivalence of nonclassical symmetries with respect to a transformation group, we completely classify the nonclassical symmetries of the corresponding potential equation. As a result, new wide classes of potential nonclassical symmetries of the fast diffusion equation are obtained. The set of known exact non-Lie solutions are supplemented with the similar ones. It is shown that all known non-Lie solutions of the fast diffusion equation are exhausted by ones which can be constructed in a regular way with the above potential nonclassical symmetries. Connection between classes of nonclassical and potential nonclassical symmetries of the fast diffusion equation is found.

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