On a quadratic Poisson algebra and integrable Lotka-Volterra systems, with solutions in terms of Lambert's W function

Autor:	van der Kamp, Peter H., McLaren, D. I., Quispel, G. R. W.
Rok vydání:	2024
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	We study a class of integrable nonhomogeneous Lotka-Volterra systems whose quadratic terms defined by an antisymmetric matrix and whose linear terms consist of three blocks. We provide the Poisson algebra of their Darboux polynomials, and prove a contraction theorem. We then use these results to classify the systems according to the number of functionally independent (and, for some, commuting) integrals. We also establish separability/solvability by quadratures, given the solutions to the 2- and 3-dimensional systems, which we provide in terms of the Lambert W function. Comment: 19 pages, 1 table, 11 references
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.14720 Zobrazit plný text záznamu View this record from Arxiv