All meromorphic solutions of a 3D Lotka-Volterra system: detecting partial integrability
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909443869900800 |
|---|---|
| author | Meng, Techheang Halburd, Rod |
| author_facet | Meng, Techheang Halburd, Rod |
| contents | For an autonomous system of ordinary differential equations, the existence of a meromorphic general solution is equivalent to the Painlevé property, which is widely used to detect integrability. We find all meromorphic solutions of a multi-parameter three-dimensional Lotka-Volterra system. Some cases correspond to particular choices of the parameters for which only some solutions are meromorphic, while the general solution is branched. The main difficulty is to prove that all meromorphic solutions have been found. The proof relies on a detailed study of local series expansions combined with value distribution results from Nevanlinna theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All meromorphic solutions of a 3D Lotka-Volterra system: detecting partial integrability Meng, Techheang Halburd, Rod Exactly Solvable and Integrable Systems 30D35 (Primary) 34M05 (Secondary) For an autonomous system of ordinary differential equations, the existence of a meromorphic general solution is equivalent to the Painlevé property, which is widely used to detect integrability. We find all meromorphic solutions of a multi-parameter three-dimensional Lotka-Volterra system. Some cases correspond to particular choices of the parameters for which only some solutions are meromorphic, while the general solution is branched. The main difficulty is to prove that all meromorphic solutions have been found. The proof relies on a detailed study of local series expansions combined with value distribution results from Nevanlinna theory. |
| title | All meromorphic solutions of a 3D Lotka-Volterra system: detecting partial integrability |
| topic | Exactly Solvable and Integrable Systems 30D35 (Primary) 34M05 (Secondary) |
| url | https://arxiv.org/abs/2412.20304 |