Quadrirational Yang-Baxter maps and the elliptic Cremona system
Exactly Solvable and Integrable Systems
2018-04-06 v1
Abstract
This paper connects the quadrirational Yang-Baxter maps, which are two-dimensional integrable discrete systems of KdV type, and the elliptic Cremona system, which is a higher analogue of discrete Painlev\'e equations associated with symmetry. This is a natural connection between integrable systems in different dimensions that is outside of the usual paradigm of reductions. Our approach is based on formulation of both systems in terms of birational Coxeter groups.
Cite
@article{arxiv.1804.01794,
title = {Quadrirational Yang-Baxter maps and the elliptic Cremona system},
author = {James Atkinson and Yasuhiko Yamada},
journal= {arXiv preprint arXiv:1804.01794},
year = {2018}
}
Comments
11 pages, 2 figures. This is a comprehensive revision of the previous (unpublished) work arXiv:1405.2745