# Entwining Yang-Baxter maps related to NLS type equations

## TL;DR

This paper constructs and analyzes birational Yang-Baxter maps derived from Darboux transformations of NLS equations, demonstrating their algebraic properties and integrability.

## Contribution

It introduces new Yang-Baxter maps from NLS-related Darboux transformations and proves their complete integrability and algebraic structures.

## Key findings

- Constructed new birational Yang-Baxter maps
- Proved their complete integrability in Liouville sense
- Analyzed algebraic properties like invariants and symplectic structures

## Abstract

We construct birational maps that satisfy the parametric set-theoretical Yang-Baxter equation and its entwining generalisation. For this purpose, we employ Darboux transformations related to integrable Nonlinear Schr\"odinger type equations and study the refactorisation problems of the product of their associated Darboux matrices. Additionally, we study various algebraic properties of the derived maps, such as invariants and associated symplectic or Poisson structures, and we prove their complete integrability in the Liouville sense.