On a quadratic Poisson algebra and integrable Lotka-Volterra systems with solutions in terms of Lambert's W function
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914996655489024 |
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| author | van der Kamp, Peter H. McLaren, D. I. Quispel, G. R. W. |
| author_facet | van der Kamp, Peter H. McLaren, D. I. Quispel, G. R. W. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14720 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a quadratic Poisson algebra and integrable Lotka-Volterra systems with solutions in terms of Lambert's W function van der Kamp, Peter H. McLaren, D. I. Quispel, G. R. W. Exactly Solvable and Integrable Systems Dynamical Systems 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. |
| title | On a quadratic Poisson algebra and integrable Lotka-Volterra systems with solutions in terms of Lambert's W function |
| topic | Exactly Solvable and Integrable Systems Dynamical Systems |
| url | https://arxiv.org/abs/2408.14720 |