On the Integrability of Classical Ruijsenaars-Schneider Model of $BC_{2}$ Type

TL;DR

This paper investigates the integrability of the classical relativistic Ruijsenaars-Schneider model of BC2 type, deriving explicit integrals of motion and Hamiltonian solutions for this specific case.

Contribution

It provides the explicit form of the extra integral of motion and Hamiltonian for the BC2 type model, advancing understanding of relativistic integrable many-body systems.

Findings

Explicit integral of motion for BC2 model derived

Hamiltonian obtained by solving functional equations

Advances the classification of integrable relativistic models

Abstract

The problem of finding most general form of the classical integrable relativistic models of many-body interaction of the $BC_{n}$ type is considered. In the simplest nontrivial case of $n=2$,the extra integral of motion is presented in explicit form within the ansatz similar to the nonrelativistic Calogero-Moser models. The resulting Hamiltonian has been found by solving the set of two functional equations.