Potential Nonclassical Symmetries and Solutions of Fast Diffusion Equation
Abstract
The fast diffusion equation 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.
Cite
@article{arxiv.math-ph/0506067,
title = {Potential Nonclassical Symmetries and Solutions of Fast Diffusion Equation},
author = {Roman O. Popovych and Olena O. Vaneeva and Nataliya M. Ivanova},
journal= {arXiv preprint arXiv:math-ph/0506067},
year = {2007}
}
Comments
13 pages, section 3 is essentially revised