On integrability of 2-dimensional $\sigma$-models of Poisson-Lie type

TL;DR

This paper presents a straightforward method to construct Lax pairs for certain 2D sigma models related to Poisson-Lie T-duality, facilitating the analysis of their integrability properties.

Contribution

It introduces a simple procedure for deriving Lax pairs in Poisson-Lie sigma models, advancing the understanding of their integrability.

Findings

Lax pairs can be systematically constructed for these models.

The method simplifies the analysis of integrability in Poisson-Lie sigma models.

Potential applications in duality and integrability studies.

Abstract

We describe a simple procedure for constructing a Lax pair for suitable 2-dimensional $\sigma$-models appearing in Poisson-Lie T-duality