Integrable systems on quad-graphs
| dc.creator | Bobenko, Alexander I. | |
| dc.creator | Suris, Yuri B. | |
| dc.date | 2001-10-04 | |
| dc.date.accessioned | 2026-07-07T05:33:42Z | |
| dc.date.available | 2026-07-07T05:33:42Z | |
| dc.description | We consider general integrable systems on graphs as discrete flat connections with the values in loop groups. We argue that a certain class of graphs is of a special importance in this respect, namely quad-graphs, the cellular decompositions of oriented surfaces with all two-cells being quadrilateral. We establish a relation between integrable systems on quad-graphs and discrete systems of the Toda type on graphs. We propose a simple and general procedure for deriving discrete zero curvature representations for integrable systems on quad-graphs, based on the principle of the three-dimensional consistency. Thus, finding a zero curvature representation is put on an algorithmic basis and does not rely on the guesswork anymore. Several examples of integrable systems on quad-graphs are considered in detail, their geometric interpretation is given in terms of circle patterns. | |
| dc.description | 29 pages, 11 figures | |
| dc.identifier | https://arxiv.org/abs/nlin/0110004 | |
| dc.identifier | http://arxiv.org/abs/nlin/0110004 | |
| dc.identifier | Internat. Math. Research Notices, 2002, Nr. 11, p.573-611 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80093 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Integrable systems on quad-graphs | |
| dc.type | text |