2024/12/29 by Meng, Techheang, Rod Halburd, Halburd, Rod
Mathematics · Physics and Astronomy · #30D35 (Primary) 34M05 (Secondary) #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Meromorphic and Entire Functions #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2412.20304
openalex publication_date 2024/12/29 · openalex created_date 2025/01/01 · openalex updated_date 2026/07/28
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.