Integrable tops and non-commutative torus

dc.creatorOlshanetsky, M.
dc.date2002-03-04
dc.date.accessioned2026-07-07T05:33:57Z
dc.date.available2026-07-07T05:33:57Z
dc.descriptionWe consider the hydrodynamics of the ideal fluid on a 2-torus and its Moyal deformations. The both type of equations have the form of the Euler-Arnold tops. The Laplace operator plays the role of the inertia-tensor. It is known that 2-d hydrodynamics is non-integrable. After replacing of the Laplace operator by a distinguish pseudo-differential operator the deformed system becomes integrable. It is an infinite rank Hitchin system over an elliptic curve with transition functions from the group of the non-commutative torus. In the classical limit we obtain an integrable analog of the hydrodynamics on a torus with the inertia-tensor operator $\bar\partial^2$ instead of the conventional Laplace operator $\partial\bar\partial$.
dc.description8 pages, espcrc2.tex, Contribution in Proc. of Int. Workshop ``Supersymmetries and Quantum Symmetries'', Sept. 21-25, 2001, Karpacz, Poland
dc.identifierhttps://arxiv.org/abs/nlin/0203003
dc.identifierhttp://arxiv.org/abs/nlin/0203003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80186
dc.subjectExactly Solvable and Integrable Systems
dc.subjectHigh Energy Physics - Theory
dc.titleIntegrable tops and non-commutative torus
dc.typetext

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