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Potential nonclassical symmetries and solutions of fast diffusion equation

By Roman O. Popovych, Nataliya M. Ivanova and Olena O. Vaneeva

Abstract

A fast diffusion equation is investigated with symmetry point of view. The set of exact non-Lie solutions constructed by M.L. Gandarias [Phys. Lett. A, 2001,V.286, 153-160] are supplemented with the similar ones. The non-classical symmetries of the corresponding potential equation are completely classified with respect to the Lie symmetry group of this equation. As a result, we obtain new wide classes of potential non-classical symmetries of the fast diffusion equation. It is shown that all known non-Lie solutions of the fast diffusion equation are exhausted by ones which can be constructed with the above potential non-classical symmetries

Year: 2007
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