Volume 20, Issue 4, December 2013, Pages 577 - 605
On Bianchi permutability of Bäcklund transformations for asymmetric quad-equations
Authors
Raphael Boll
Institut für Mathematik, MA 7-2, Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin, Germanyboll@math.tu-berlin.de
Received 17 June 2013, Accepted 31 October 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.865829How to use a DOI?
- Keywords
- Quad-equation; Bäcklund transformation; Bianchi permutability; 3D consistency; integrability
- Abstract
We prove the Bianchi permutability (existence of superposition principle) of Bäcklund transformations for asymmetric quad-equations. Such equations and their Bäcklund transformations form 3D consistent systems of a priori different equations. We perform this proof by using 4D consistent systems of quad-equations, the structural insights through biquadratics patterns and the consideration of super-consistent eight-tuples of quad-equations on decorated cubes.
- Copyright
- © 2013 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/).
Cite this article
TY - JOUR AU - Raphael Boll PY - 2021 DA - 2021/01/06 TI - On Bianchi permutability of Bäcklund transformations for asymmetric quad-equations JO - Journal of Nonlinear Mathematical Physics SP - 577 EP - 605 VL - 20 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.865829 DO - 10.1080/14029251.2013.865829 ID - Boll2021 ER -