On the Lagrangian 1-Form Structure of the Hyperbolic Calogero-Moser System

Abstract

In this work, we present another example of the Lagrangian 1-form structure for the hy- perbolic Calogero-Moser system both in discrete-time level and continuous-time level. The discrete-time hyperbolic Calogero-Moser system is obtained by considering pole-reduction of the semi-discrete Kadomtsev-Petviashvili (KP) equation. The key relation called the discrete-time closure relation is directly obtained from the compatibility between the temporal Lax matrices. The continuous-time hierarchy of the hyperbolic Calogero-Moser system is obtained through two successive continuum limits. The continuous-time closure relation, which is a consequence of continuum limits on the discrete-time one, is also shown to hold.

25 pages, 5 figures

References in corpus (3)

• Variational formulation of commuting Hamiltonian flows: multi-time Lagrangian 1-forms
• An integrable multicomponent quad equation and its Lagrangian formulation
• Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Toda-type systems

Cited by in corpus (1)

• Quantum integrability: Lagrangian 1-form case