From auto-B\"acklund transformations to auto-B\"acklund transformations, and torqued ABS equations
Exactly Solvable and Integrable Systems
2021-09-09 v2
Abstract
We provide a method which takes an auto-B\"acklund transformation (auto-BT) and produces another auto-BT for a different equation. We apply the method to the natural auto-BTs for the ABS quad equations, which gives rise to torqued versions of ABS equations and explains the origin of each auto-BT listed in [J. Atkinson, J. Phys. A: Math. Theor. 41 (2008) 135202]. The method is also applied to non-natural auto-BTs for ABS equations, which yields 3D consistent cubes which have not been found in [R. Boll, J. Nonl. Math. Phys. 18 (2011) 337--365], and to a multi-quadratic ABS* equation giving rise to a multi-quartic equation.
Cite
@article{arxiv.2102.11668,
title = {From auto-B\"acklund transformations to auto-B\"acklund transformations, and torqued ABS equations},
author = {Dan-da Zhang and Da-jun Zhang and Peter H. van der Kamp},
journal= {arXiv preprint arXiv:2102.11668},
year = {2021}
}
Comments
19 pages, 8 figures, 5 tables, accepted for publication by Mathematical Physics, Analysis and Geometry