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. |
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Rok vydání: | 2024 |
Předmět: | |
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 |
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