On the Lagrangian structure of Calogero's Goldfish model
Exactly Solvable and Integrable Systems
2014-09-26 v1 Mathematical Physics
math.MP
Abstract
The discrete-time rational Calogero's goldfish system is obtained from the Ansatz Lax pair. The discrete-time Lagrangians of the system possess the discrete-time 1-form structure as those in the discrete-time Calogero-Moser system and discrete-time Ruijsenaars-Schneider system. Performing two steps of continuum limits, we obtain Lagrangian hierarchy for the system. Expectingly, the continuous-time Lagrange 1-form structure of the system holds. Furthermore, the connection to the lattice KP systems is also established.
Keywords
Cite
@article{arxiv.1409.7168,
title = {On the Lagrangian structure of Calogero's Goldfish model},
author = {Umpon Jairuk and Sikarin Yoo-Kong and Monsit Tanasittikosol},
journal= {arXiv preprint arXiv:1409.7168},
year = {2014}
}
Comments
20 pages, 3 figures