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Title: On the Lagrangian structure of Calogero's Goldfish model
Authors: U. Jairuk
S. Yoo-Kong
M. Tanasittikosol
ผศ.ดร.สิขรินทร์ อยู่คง
Keywords: Calogero’s goldfish
multitime Lagrangian 1-forms
closure relation
Issue Date: 2015
Citation: Jairuk, U., Yoo-Kong, S. & Tanasittikosol, M. The Lagrangian structure of Calogero’s goldfish model. Theor Math Phys 183, 665–683 (2015).
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.
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