2003/07/24 by M. A. Olshanetsky, Olshanetsky, M.
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.nlin/0307044
openalex publication_date 2003/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a large N limit of the Hitchin type integrable systems. The first system is the elliptic rotator on GLN 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 consider the elliptic Calogero-Moser system on the group of the non-commutative torus and consider the systems that arise after the reduction to the loop group.