On the r-matrix structure of the hyperbolic BC(n) Sutherland model

TL;DR

This paper constructs a dynamical r-matrix for the hyperbolic BC(n) Sutherland model using symplectic reduction, and explores its Lax representation and Hamiltonian dynamics.

Contribution

It introduces a new dynamical r-matrix for the hyperbolic BC(n) Sutherland model with three coupling constants within a symplectic reduction framework.

Findings

Constructed a dynamical r-matrix for the model.

Established the equivalence of Lax representation and Hamiltonian equations.

Analyzed the model's integrability properties.

Abstract

Working in a symplectic reduction framework, we construct a dynamical r-matrix for the classical hyperbolic BC(n) Sutherland model with three independent coupling constants. We also examine the Lax representation of the dynamics and its equivalence with the Hamiltonian equation of motion.