Olena VANEEVA, Roman POPOVYCH and Nataliya IVANOVA
Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivs'ka Str.,
01601 Kyiv,
E-mail: vaneeva@imath.kiev.ua, rop@imath.kiev.ua, ivanova@imath.kiev.ua

Potential non-classical symmetries and exact solutions of fast diffusion equation

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, 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.

For details see math-ph/0506067