Classification of 3D consistent quad-equations
Exactly Solvable and Integrable Systems
2015-05-20 v2
Abstract
We consider 3D consistent systems of six independent quad-equations assigned to the faces of a cube. The well-known classification of 3D consistent quad-equations, the so-called ABS-list, is included in this situation. The extension of these equations to the whole lattice Z^3 is possible by reflecting the cubes. For every quad-equation we will give at least one system included leading to a B\"acklund transformation and a zero-curvature representation which means that they are integrable.
Cite
@article{arxiv.1009.4007,
title = {Classification of 3D consistent quad-equations},
author = {Raphael Boll},
journal= {arXiv preprint arXiv:1009.4007},
year = {2015}
}
Comments
31 pages