Integrable tops and non-commutative torus
| dc.creator | Olshanetsky, M. | |
| dc.date | 2002-03-04 | |
| dc.date.accessioned | 2026-07-07T05:33:57Z | |
| dc.date.available | 2026-07-07T05:33:57Z | |
| dc.description | We 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.description | 8 pages, espcrc2.tex, Contribution in Proc. of Int. Workshop ``Supersymmetries and Quantum Symmetries'', Sept. 21-25, 2001, Karpacz, Poland | |
| dc.identifier | https://arxiv.org/abs/nlin/0203003 | |
| dc.identifier | http://arxiv.org/abs/nlin/0203003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80186 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Integrable tops and non-commutative torus | |
| dc.type | text |