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TMF, 2015, Volume 183, Number 2, Pages 254–273 (Mi tmf8800)  

This article is cited in 3 scientific papers (total in 3 papers)

The Lagrangian structure of Calogero's goldfish model

U. P. Jairuk, S. Yoo-Kong, M. Tanasittikosol

Department of Physics, Faculty of Science, King Mongkut's University of Technology Thonburi

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.

Keywords: Calogero's goldfish, multitime Lagrangian 1-forms, closure relation

Funding Agency Grant Number
Thailand Research Fund (TRF) TRG5680081


DOI: https://doi.org/10.4213/tmf8800

Full text: PDF file (531 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 183:2, 665–683

Bibliographic databases:

PACS: -
Received: 07.10.2014

Citation: U. P. Jairuk, S. Yoo-Kong, M. Tanasittikosol, “The Lagrangian structure of Calogero's goldfish model”, TMF, 183:2 (2015), 254–273; Theoret. and Math. Phys., 183:2 (2015), 665–683

Citation in format AMSBIB
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\pages 665--683
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  • https://doi.org/10.4213/tmf8800
  • http://mi.mathnet.ru/eng/tmf/v183/i2/p254

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. K. Surawuttinack, S. Yoo-Kong, M. Tanasittikosol, “Multiplicative form of the Lagrangian”, Theoret. and Math. Phys., 189:3 (2016), 1693–1711  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. F. Calogero, “Three new classes of solvable $N$-body problems of goldfish type with many arbitrary coupling constants”, Symmetry-Basel, 8:7 (2016), 53  crossref  mathscinet  isi  scopus
    3. U. Jairuk, M. Tanasittikosol, “On the Lagrangian 1-form structure of the hyperbolic Calogero - Moser system”, Rep. Math. Phys., 79:3 (2017), 299–330  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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