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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 199
  • Publication Date: 2020
  • Doi Number: 10.1016/j.na.2020.111947
  • Title of Journal : NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Abstract

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.