Abstract
In this study, we investigate first integrals and exact solutions of the Ermakov-Pinney equation. Firstly, the Lagrangian for the equation is constructed and then the determining equations are obtained based on the Lagrangian approach. Noether symmetry classification is implemented, the first integrals, conservation laws are obtained and classified. This classification includes Noether symmetries and first integrals with respect to different choices of external potential function. Furthermore, the time independent integrals and analytical solutions are obtained by using the modified Prelle-Singer procedure as a different approach. Additionally, for the investigation of conservation laws of the equation, we present the mathematical connections between the λ-symmetries, Lie point symmetries and the modified Prelle-Singer procedure. Finally, new Lagrangian and Hamiltonian forms of the equation are determined.
| Original language | English |
|---|---|
| Pages (from-to) | 753-764 |
| Number of pages | 12 |
| Journal | Discrete and Continuous Dynamical Systems - Series S |
| Volume | 11 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Aug 2018 |
Keywords
- Classification
- First integral
- Invariant solution
- Lagrangian and Hamiltonian description
- Noether theory
- Prelle-Singer method
- λ-symmetry.