Journal of Nonlinear Mathematical Physics

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
https://doi.org/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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
20 - 4
Pages
577 - 605
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2013.865829How to use a DOI?
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  - https://doi.org/10.1080/14029251.2013.865829
ID  - Boll2021
ER  -