{"paper":{"title":"Integrable reductions of the dressing chain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Charalampos Evripidou, Pavlos Kassotakis, Pol Vanhaecke","submitted_at":"2019-03-07T12:35:50Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02876","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}