On the construction of elliptic solutions of integrable birational maps
Exactly Solvable and Integrable Systems
2019-11-11 v3 Mathematical Physics
math.MP
Abstract
We present a systematic technique to find explicit solutions of birational maps, provided that these solutions are given in terms of elliptic functions. The two main ingredients are: (i) application of classical addition theorems for elliptic functions, and (ii) experimental technique to detect an algebraic curve containing a given sequence of points in a plane. These methods are applied to Kahan-Hirota-Kimura discretizations of the periodic Volterra chains with 3 and 4 particles.
Keywords
Cite
@article{arxiv.1409.1741,
title = {On the construction of elliptic solutions of integrable birational maps},
author = {Matteo Petrera and Andreas Pfadler and Yuri B. Suris},
journal= {arXiv preprint arXiv:1409.1741},
year = {2019}
}
Comments
26 pp. In the new version an Appendix by Yuri N. Fedorov is added, which treats the discrete time periodic Volterra chain with 3 particles by an alternative method, appendix by Yuri N. Fedorov