Integrable open elliptic Toda chain with boundaries

TL;DR

This paper constructs an integrable open elliptic Toda chain with boundary conditions by utilizing the Lax matrix factorization and establishing gauge equivalence with the XYZ chain, expanding the class of integrable models.

Contribution

It introduces a novel method to incorporate boundary terms into the classical elliptic Toda chain using Lax matrix factorization and gauge transformations.

Findings

Successfully constructed an open elliptic Toda chain with boundaries.

Established gauge equivalence with the XYZ chain.

Extended integrable models with boundary conditions.

Abstract

In this letter we discuss the classical integrable elliptic Toda chain proposed by I. Krichever. Our goal is to construct an open elliptic Toda chain with boundary terms. This is achieved using the factorized form of the Lax matrix and gauge equivalence with the XYZ chain.