Geodesic
One-parameter discrete-time Calogero–Moser system
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 415-429 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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