2005/06/30 by Roman O. Popovych, Olena Vaneeva, Olena O. Vaneeva +1
Mathematics · Physics and Astronomy · #Connection (principal bundle) #Diffusion #Diffusion equation #Equivalence (formal languages) #Geometry #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Spacetime symmetries #Symmetry (geometry) #Symmetry group #math-ph #math.MP #msc:35C05 #msc:35K57 #nlin.SI
paper · pdf · doi:10.1016/j.physleta.2006.10.015
published as Phys. Lett. A 362 (2007) 166-173 · 13 pages, section 3 is essentially revised
openalex publication_date 2006/10/15 · arxiv created 2007/01/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The fast diffusion equation ut=(u-1ux)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.