Invariance of second order ordinary differential equations under two-dimensional affine subalgebras of Ermakov-Pinney Lie algebra

Carinena J. F., Gungor F., Torres P. J.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.199, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 199
  • Publication Date: 2020
  • Doi Number: 10.1016/
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Istanbul Technical University Affiliated: Yes


Using the only admissible rank-two realisations of the Lie algebra of the affine group in one dimension in terms of the Lie algebra of Lie symmetries of the Ermakov-Pinney (EP) equation, some classes of second order nonlinear ordinary differential equations solvable by reduction method are constructed. One class includes the standard EP equation as a special case. A new EP equation with a perturbed potential but admitting the same solution formula as EP itself arises. The solution of the dissipative EP equation is also discussed. (C) 2020 Elsevier Ltd. All rights reserved.