Geodesic
The Lagrangian structure of Calogero's goldfish model
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 2, pp. 254-273 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{TMF_2015_183_2_a4,
     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},
     year = {2015},
     volume = {183},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a4/}
}
TY  - JOUR
AU  - U. P. Jairuk
AU  - S. Yoo-Kong
AU  - M. Tanasittikosol
TI  - The Lagrangian structure of Calogero's goldfish model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2015
SP  - 254
EP  - 273
VL  - 183
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a4/
LA  - ru
ID  - TMF_2015_183_2_a4
ER  - 
%0 Journal Article
%A U. P. Jairuk
%A S. Yoo-Kong
%A M. Tanasittikosol
%T The Lagrangian structure of Calogero's goldfish model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2015
%P 254-273
%V 183
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2015_183_2_a4/
%G ru
%F TMF_2015_183_2_a4
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/

[1] S. B. Lobb, F. W. Nijhoff, J. Phys. A: Math. Theor., 42:45 (2009), 454013, 18 pp., arXiv: 0903.4086 | DOI | MR | Zbl

[2] S. B. Lobb, F. W. Nijhoff, J. Phys. A: Math. Theor., 43:7 (2010), 072003, 11 pp. | DOI | MR | Zbl

[3] S. B. Lobb, F. W. Nijhoff, G. R. W. Quispel, J. Phys. A: Math. Theor., 42:47 (2009), 472002, 11 pp. | DOI | MR | Zbl

[4] F. Calogero, J. Math. Phys., 10:12 (1969), 2191–2196 | DOI

[5] F. Calogero, J. Math. Phys., 12:3 (1971), 419–436 | DOI | MR

[6] S. Yoo-Kong, S. B. Lobb, F. W. Nijhoff, J. Phys. A: Math. Theor., 44:36 (2011), 365203, 39 pp. | DOI | MR | Zbl

[7] S. Yoo-Kong, F. W. Nijhoff, Discrete-time Ruijsenaars–Schneider system and Lagrangian 1-form structure, arXiv: 1112.4576

[8] Yu. B. Suris, J. Geom. Mech., 5:3 (2013), 365–379 | DOI | MR | Zbl

[9] R. Boll, M. Petrera, Yu. B. Suris, J. Phys. A: Math. Theor., 46:27 (2013), 275204, 26 pp., arXiv: 1408.2405 | DOI | MR | Zbl

[10] F. Calogero, Phys. D, 152–153 (2001), 78–84 | DOI | MR | Zbl

[11] Yu. B. Suris, J. Nonlinear Math. Phys., 12:supp.\;1 (2005), 633–647 | DOI | MR

[12] F. W. Nijhoff, P. Gen-Di, Phys. Lett. A, 191:1–2 (1994), 101–107 | DOI | MR | Zbl

[13] F. W. Nijhoff, O. Ragnisco, V. Kuznetsov, Commun. Math. Phys., 176:3 (1996), 681–700 | DOI | MR | Zbl

[14] F. W. Nijhoff, H. W. Capel, G. L. Wiersma, G. R.Ẇ. Quispel, Phys. Lett. A, 105:6 (1984), 267–272 | DOI | MR

[15] I. Ya. Dorfman, F. W. Nijhoff, Phys. Lett. A, 157:2–3 (1991), 107–112 | DOI | MR

[16] F. W. Nijhoff, H. W. Capel, G. L. Wiersma, “Integrable lattice systems in two and three dimensions”, Geometric Aspects of the Einstein Equations and Integrable Systems (Scheveningen, The Netherlands, August 26–31, 1984), Lecture Notes in Physics, 239, ed. R. Martini, Springer, Berlin–New York, 1985, 263–302 | DOI | MR | Zbl

[17] R. Hirota, J. Phys. Soc. Japan, 50:11 (1981), 3785–3791 | DOI | MR