Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Meng, Techheang, Halburd, Rod
Institution: University College London
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405955748