Integrable systems on quad-graphs

Details Integrable systems on quad-graphs Integrable systems on quad-graphs

2001-10-04

arxiv.org/abs/nlin/0110004v1

Internat. Math. Research Notices, 2002, Nr. 11, p.573-611

Nonlinear Sciences

Exactly Solvable and Integrable Systems

29 pages, 11 figures

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Integrable systems on quad-graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Integrable systems on quad-graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integrable systems on quad-graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-417309