English

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.

Keywords

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

R2 v1 2026-06-21T16:16:41.212Z