On the Generalizations of the Kummer–Schwarz Equation. (March 2020)

• Record Type: Journal Article
• Authors: Bozhkov, Yuri Dimitrov; da Conceição, Pammela Ramos
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: 76M60 -- 58J70 -- 35A30 -- 70G65; Kummer–Schwarz equation -- Lie point symmetry -- Group classification -- Equivalence group -- Linearization of third-order ODE; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111691
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We carry out complete group classifications of two non-homogeneous generalizations of the Kummer–Schwarz equation. In particular we prove that the symmetry algebra for one of them is s l ( 2, R ) ⊕ s l ( 2, R ) and that it can be mapped by an equivalence transformation to the homogeneous Kummer–Schwarz equation. For this purpose we calculate the continuous equivalence group for that equation. We also study the linearization of the considered equations.