2004/02/29 by Roman O. Popovych, Roman O Popovych, Nataliya M. Ivanova +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #math-ph #math.MP #msc:35C05 #msc:35K57 #msc:58J70 #nlin.SI
paper · pdf · doi:10.1088/0305-4470/38/14/006
published as J. Phys. A: Math. Gen., 2005, V.38, N 14, 3145-3155 · 10 pages
arxiv created 2005/03/16 · openalex publication_date 2005/03/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Potential equivalence transformations (PETs) are effectively applied to a class of nonlinear diffusion–convection equations. For this class, all possible potential symmetries are classified and a theorem on their connection with point symmetries via PETs is also proved. It is shown that the known nonlocal transformations between equations under consideration are nothing but PETs. The action of PETs on sets of exact solutions of a fast diffusion equation is investigated.