Geodesic
The~Lagrangian structure of Calogero's goldfish model
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 2, pp. 254-273

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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.
Keywords: Calogero's goldfish, multitime Lagrangian 1-forms, closure relation. 
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     author = {U. P. Jairuk and S. Yoo-Kong and M. Tanasittikosol},
     title = {The~Lagrangian structure of {Calogero's} goldfish model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {254--273},
     publisher = {mathdoc},
     volume = {183},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a4/}
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U. P. Jairuk; S. Yoo-Kong; M. Tanasittikosol. The~Lagrangian structure of Calogero's goldfish model. Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 2, pp. 254-273. http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a4/