{"paper":{"title":"Large $N$ limit of integrable models","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"M.Olshanetsky","submitted_at":"2003-07-24T08:55:50Z","abstract_excerpt":"We consider a large $N$ limit of the Hitchin type integrable systems.\n The first system is the elliptic rotator on $GL_N$ that corresponds to the Higgs bundle of degree one over an elliptic curve with a marked point. This system is gauge equivalent to the $N$-body elliptic Calogero-Moser system, that is derived from the Higgs bundle of degree zero over the same curve. The large $N$ limit of the former system is the integrable rotator on the group of the non-commutative torus. Its classical limit leads to the integrable modification of 2d hydrodynamics on the two-dimensional torus. We also cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0307044","kind":"arxiv","version":1},"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"}