On the complete integrability of a nonlinear oscillator from group theoretical perspective
Abstract
In this paper, we investigate the integrability aspects of a physically important nonlinear oscillator which lacks sufficient number of Lie point symmetries but can be integrated by quadrature. We explore the hidden symmetry, construct a second integral, and derive the general solution of this oscillator by employing the recently introduced λ-symmetry approach and thereby establish the complete integrability of this nonlinear oscillator equation from a group theoretical perspective.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- July 2012
- DOI:
- 10.1063/1.4731238
- arXiv:
- arXiv:1207.4945
- Bibcode:
- 2012JMP....53g3504B
- Keywords:
-
- 03.65.Ge;
- 02.30.Rz;
- 02.30.-f;
- Solutions of wave equations: bound states;
- Integral equations;
- Function theory analysis;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 15 pages