2008/05/15 by Nataliya M. Ivanova, N. M. Ivanova, R. O. Popovych +2 · 11 citations
Mathematics · Physics and Astronomy · #Conservation law #Differential Equations and Numerical Methods #Diffusion #Economics #Geometry #Homogeneous space #Law #Law and economics #Mathematical analysis #Mathematical economics #Mathematics #Nonlinear Waves and Solitons #Physics #Political science #Quantum chaos and dynamical systems #Statistical physics #Theoretical physics #Thermodynamics #math-ph #math.MP #msc:35A30 #msc:35K57 #nlin.SI
paper · pdf · doi:10.1088/1751-8113/41/23/235201
published in Journal of Physics A Mathematical and Theoretical 41(23), 235201 (Institute of Physics) · 19 pages; minor corrections
openalex publication_date 2008/05/15 · arxiv created 2008/11/16 · arxiv updated 2009/12/01 · openalex created_date 2017/10/20 · openalex updated_date 2026/08/05
We show that the so-called hidden potential symmetries considered in a recent paper [Gandarias M., Physica A, 2008, V.387, 2234-2242] are ordinary potential symmetries that can be obtained using the method introduced by Bluman and collaborators. In fact, these are simplest potential symmetries associated with potential systems which are constructed with single conservation laws having no constant characteristics. Furthermore we classify the conservation laws for classes of porous medium equations and then using the corresponding conserved (potential) systems we search for potential symmetries. This is the approach one needs to adopt in order to determine the complete list of potential symmetries. The provenance of potential symmetries is explained for the porous medium equations by using potential equivalence transformations. Point and potential equivalence transformations are also applied to deriving new results on potential symmetries and corresponding invariant solutions from known ones. In particular, in this way the potential systems, potential conservation laws and potential symmetries of linearizable equations from the classes of differential equations under consideration are exhaustively described. Infinite series of infinite-dimensional algebras of potential symmetries are constructed for such equations.