The Lagrangian structure of Calogero’s goldfish model
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Publication Details
Author list: Jairuk U., Yoo-Kong S., Tanasittikosol M.
Publisher: Springer
Publication year: 2015
Journal: Theoretical and Mathematical Physics (0040-5779)
Volume number: 183
Issue number: 2
Start page: 665
End page: 683
Number of pages: 19
ISSN: 0040-5779
eISSN: 1573-9333
Languages: English-Great Britain (EN-GB)
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Abstract
From a Lax pair ansatz, we obtain the discrete-time rational Calogero goldfish system. The discrete-time Lagrangians of the system have a discrete-time 1-form structure similar to the Lagrangians in the discrete-time Calogero-Moser system and the discrete-time Ruijsenaars-Schneider system. We obtain the Lagrangian hierarchy for the system as a result of a two-step passage to the continuum limit. As expected, the continuous-time Lagrangian preserves the 1-form structure. We establish a connection with the Kadomtsev-Petviashvili lattice systems. ฉ 2015, Pleiades Publishing, Ltd.
Keywords
Calogero’s goldfish, closure relation, multitime Lagrangian 1-forms
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