Next Article In Issue>
Volume 18, Issue 3, September 2011, Pages 337 - 365
Classification of 3D Consistent Quad-Equations
Authors
Raphael Boll
Institut für Mathematik, MA 7-2, Technische Universität Berlin, Str. des 17. Juni 136 10623 Berlin, Germany,boll@math.tu-berlin.de
Received 3 November 2010, Accepted 11 December 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001647How to use a DOI?
- Keywords
- Integrability; quad-graph; multidimensional consistency; zero curvature representation; Bäcklund transformation; Möbius transformation
- Abstract
We consider 3D consistent systems of six possibly different 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 ℤ3 is possible by reflecting the cubes. For every quad-equation we will give at least one system included leading to a Bäcklund transformation and a zero-curvature representation which means that they are integrable.
- Copyright
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Next Article In Issue>
Cite this article
TY - JOUR AU - Raphael Boll PY - 2021 DA - 2021/01/07 TI - Classification of 3D Consistent Quad-Equations JO - Journal of Nonlinear Mathematical Physics SP - 337 EP - 365 VL - 18 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001647 DO - 10.1142/S1402925111001647 ID - Boll2021 ER -