Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-12-20
Nonlinear Sciences
Exactly Solvable and Integrable Systems
32 pages
Scientific paper
We study the Lagrange formalism of the (rational) Ruijsenaars-Schneider (RS) system, both in discrete time as well as in continuous time, as a second 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 present the full solution based on the commutativity of the discrete-time flows. The closure relation can be established by using the equations of motion. The connection with the KP systems is also studied. Performing successive continuum limits on the RS system, we establish the Lagrange 1-form structure for the corresponding continuum case of the RS model.
Nijhoff Frank
Yoo-Kong Sikarin
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