English

On the Lagrangian 1-Form Structure of the Hyperbolic Calogero-Moser System

Exactly Solvable and Integrable Systems 2017-08-23 v1 Mathematical Physics math.MP

Abstract

In this work, we present another example of the Lagrangian 1-form structure for the hy- perbolic Calogero-Moser system both in discrete-time level and continuous-time level. The discrete-time hyperbolic Calogero-Moser system is obtained by considering pole-reduction of the semi-discrete Kadomtsev-Petviashvili (KP) equation. The key relation called the discrete-time closure relation is directly obtained from the compatibility between the temporal Lax matrices. The continuous-time hierarchy of the hyperbolic Calogero-Moser system is obtained through two successive continuum limits. The continuous-time closure relation, which is a consequence of continuum limits on the discrete-time one, is also shown to hold.

Keywords

Cite

@article{arxiv.1601.04799,
  title  = {On the Lagrangian 1-Form Structure of the Hyperbolic Calogero-Moser System},
  author = {Umpon Jairuk and Sikarin Yoo-Kong and Monsit Tanasittikosol},
  journal= {arXiv preprint arXiv:1601.04799},
  year   = {2017}
}

Comments

25 pages, 5 figures