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

Peter H. van der Kamp; D. I. McLaren; G. R. W. Quispel

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arXiv · 2408.14720

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

Peter H. van der Kamp·D. I. McLaren·G. R. W. Quispel

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Abstract

We study a class of integrable nonhomogeneous Lotka-Volterra systems whose quadratic terms are 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.

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Peter H. van der Kamp, D. I. McLaren, G. R. W. Quispel. 2024-08-27. On a quadratic Poisson algebra and integrable Lotka-Volterra systems with solutions in terms of Lambert's W function. https://arxiv.org/abs/2408.14720

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