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arXiv · 1601.04799

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

Umpon Jairuk·Sikarin Yoo-Kong·Monsit Tanasittikosol
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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.

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Umpon Jairuk, Sikarin Yoo-Kong, Monsit Tanasittikosol. 2016-01-19. On the Lagrangian 1-Form Structure of the Hyperbolic Calogero-Moser System. https://doi.org/10.1016/s0034-4877(17)30046-0

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