On Bianchi permutability of B\"acklund transformations for asymmetric quad-equations
Exactly Solvable and Integrable Systems
2013-05-30 v2 Mathematical Physics
math.MP
Abstract
We prove the Bianchi permutability (existence of superposition principle) of B\"acklund transformations for asymmetric quad-equations. Such equations and there B\"acklund 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.
Keywords
Cite
@article{arxiv.1211.4374,
title = {On Bianchi permutability of B\"acklund transformations for asymmetric quad-equations},
author = {Raphael Boll},
journal= {arXiv preprint arXiv:1211.4374},
year = {2013}
}
Comments
33 pages, 23 figures