2023/05/29 by Jairuk, Umpon, Yoo-Kong, Sikarin
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2305.18168
We present a new type of integrable one-dimensional many-body systems called a one-parameter Calogero-Moser (CM) system. In the discrete level, the Lax pairs with a parameter are introduced and, of course, the discrete-time equations of motion are obtained as well as their corresponding discrete-time Lagrangian. The integrability feature of this new system can be captured through the discrete Lagrangian closure relation by employing a connection with the temporal Lax matrices of the discrete-time Ruijsenaars-Schneider (RS) system, exact solution, and the existence of the classical r-matrix. Under the appropriate limit on the parameter, which in this case is approaching zero, the standard CM system is retrieved both discrete-time and continuous-time.