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, cilt.199, 2020 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 199
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1016/j.na.2020.111947
  • Dergi Adı: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Özet

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.