One-parameter discrete-time Calogero--Moser system
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 415-429
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We present a new type of integrable one-dimensional many-body systems called a one-parameter Calogero–Moser system. At the discrete level, the Lax pairs with a parameter are introduced and the discrete-time equations of motion are obtained as together with the corresponding discrete-time Lagrangian. The integrability property of this new system can be expressed in terms of the discrete Lagrangian closure relation by using a connection with the temporal Lax matrices of the discrete-time Ruijsenaars–Schneider system, an exact solution, and the existence of a classical $r$-matrix. As the parameter tends to zero, the standard Calogero–Moser system is recovered in both discrete-time and continuous-time forms.
Keywords:
one-parameter, discrete-time Calogero–Moser system, discrete-time Ruijsenaars–Schneider system, closure relation.
@article{TMF_2024_218_3_a0,
author = {U. Jairuk and S. Yoo-Kong},
title = {One-parameter discrete-time {Calogero--Moser} system},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {415--429},
publisher = {mathdoc},
volume = {218},
number = {3},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2024_218_3_a0/}
}
U. Jairuk; S. Yoo-Kong. One-parameter discrete-time Calogero--Moser system. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 415-429. http://geodesic.mathdoc.fr/item/TMF_2024_218_3_a0/