# Elliptic solutions of the Toda lattice with constraint of type B and deformed Ruijsenaars-Schneider system

## TL;DR

This paper investigates elliptic solutions of a constrained Toda lattice, linking their pole dynamics to a deformed Ruijsenaars-Schneider system, and proposes an extension to a field theory.

## Contribution

It derives equations of motion for elliptic solutions of a constrained Toda lattice and connects them to a deformed Ruijsenaars-Schneider system, including a new spectral curve analysis.

## Key findings

- Pole dynamics described by deformed Ruijsenaars-Schneider system
- Established a Manakov triple representation for the system
- Proposed an extension to a field theory for elliptic solutions

## Abstract

We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars-Schneider system. We find its commutation representation in the form of the Manakov triple and study properties of the spectral curve. By studying more general elliptic solutions (elliptic families), we also suggest an extension of the deformed Ruijsenaars-Schneider system to a field theory.