On the lagrangian 1-form structure of the hyperbolic calogero–moser system

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Author list: Jairuk U., Tanasittikosol M., Yoo-Kong S.

Publisher: Elsevier

Publication year: 2017

Journal: Reports on Mathematical Physics (0034-4877)

Volume number: 79

Issue number: 3

Start page: 299

End page: 330

Number of pages: 32

ISSN: 0034-4877

eISSN: 1879-0674

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85024862813&doi=10.1016%2fS0034-4877%2817%2930046-0&partnerID=40&md5=c35cd31db22ec4bc7686ba8f6ccf9987

Languages: English-Great Britain (EN-GB)

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Abstract

In this work, we present the Lagrangian 1-form structure of the hyperbolic Calogero–Moser system in both 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. Furthermore, it is shown that the hyperbolic Calogero–Moser system possesses the key relation, known as the discrete-time closure relation. This relation is a consequence of the compatibility property of the temporal Lax matrices. The continuous-time hierarchy of the hyperbolic Calogero–Moser system is obtained by taking two successive continuum limits, namely, the skewed limit and full limit. With these successive limits, the continuous-time closure relation is also obtained and is shown to hold at the continuous level. © 2017 Polish Scientific Publishers

Keywords

hyperbolic Calogero–Moser system