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- W2922082875 abstract "In this paper we construct a family of integrable reductions of the dressing chain, described in its Lotka-Volterra form. For each $k,ninmathbb N$ with $ngeqslant 2k+1$ 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." @default.
- W2922082875 created "2019-03-22" @default.
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- W2922082875 date "2019-03-07" @default.
- W2922082875 modified "2023-09-27" @default.
- W2922082875 title "Integrable reductions of the dressing chain" @default.
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