2011/12/20 by Sikarin Yoo-Kong, Frank Nijhoff, Yoo-Kong, Sikarin +1 · 1 citation
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1112.4576
openalex publication_date 2011/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Lagrange formalism of the (rational) Ruijsenaars-Schneider (RS) system, both in discrete time as well as in continuous time, as a further example of a Lagrange 1-form structure in the sense of the recent paper [24]. The discrete-time model of the RS system was established some time ago arising via an Ansatz of a Lax pair, and was shown to lead to an exactly integrable correspondence (multivalued map)[15]. In this paper we consider an extended system representing a family of commuting flows of this type, and establish a connection with the lattice KP system. In the Lagrangian 1-form structure of this extended model, the closure relation is verified making use of the equations of motion. Performing successive continuum limits on the RS system, we establish the Lagrange 1-form structure for the corresponding continuum case of the RS model.