Integrable reductions of the dressing chain
| Autor: | Pol Vanhaecke, Charalampos A. Evripidou, Pavlos Kassotakis |
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| Rok vydání: | 2019 |
| Předmět: |
Combinatorics
Physics Computational Mathematics Reduction (recursion theory) Nonlinear Sciences - Exactly Solvable and Integrable Systems Integrable system Chain (algebraic topology) First integrals Computational Mechanics FOS: Physical sciences Exactly Solvable and Integrable Systems (nlin.SI) 53D17 70H06 |
| DOI: | 10.48550/arxiv.1903.02876 |
| Popis: | In this paper we construct a family of integrable reductions of the dressing chain, described in its Lotka-Volterra form. For each $k,n\in\mathbb N$ with $n\geqslant 2k+1$ we obtain a Lotka-Volterra system $\hbox{LV}_b(n,k)$ on $\mathbb R^n$ which is a deformation of the Lotka-Volterra system $\hbox{LV}(n,k)$, which is itself an integrable reduction of the $2m+1$-dimensional Bogoyavlenskij-Itoh system $\hbox{LV}(2m+1,m)$, where $m=n-k-1$. We prove that $\hbox{LV}_b(n,k)$ is both Liouville and non-commutative integrable, with rational first integrals which are deformations of the rational first integrals of $\hbox{LV}(n,k)$. We also construct a family of discretizations of $\hbox{LV}_b(n,0)$, including its Kahan discretization, and we show that these discretizations are also Liouville and superintegrable. Comment: 35 pages |
| Databáze: | OpenAIRE |
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