Potential Nonclassical Symmetries and Solutions of Fast Diffusion Equation

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dc.creatorPopovych, Roman O.
dc.creatorVaneeva, Olena O.
dc.creatorIvanova, Nataliya M.
dc.date2005-06-26
dc.date2007-01-18
dc.date.accessioned2026-07-07T07:41:28Z
dc.date.available2026-07-07T07:41:28Z
dc.descriptionThe 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.
dc.description13 pages, section 3 is essentially revised
dc.identifierhttps://arxiv.org/abs/math-ph/0506067
dc.identifierhttp://arxiv.org/abs/math-ph/0506067
dc.identifierPhys. Lett. A 362 (2007) 166-173
dc.identifierdoi:10.1016/j.physleta.2006.10.015
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122123
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.subject35K57; 35C05
dc.titlePotential Nonclassical Symmetries and Solutions of Fast Diffusion Equation
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