From Yang-Baxter maps to integrable quad maps and recurrences

TL;DR

This paper connects Yang-Baxter maps to integrable quad equations and recurrences, revealing transformations and solvable systems derived from known solutions.

Contribution

It introduces Miura-type transformations linking Yang-Baxter maps to integrable quad equations and constructs non-autonomous solvable recurrences from these maps.

Findings

Miura-type transformations relate Yang-Baxter maps to known integrable quad equations

Constructs non-autonomous solvable recurrences of order two from Yang-Baxter maps

Establishes a systematic method to derive integrable systems from Yang-Baxter solutions

Abstract

Starting from known solutions of the functional Yang-Baxter equations, we exhibit Miura type of transformations leading to various known integrable quad equations. We then construct, from the same list of Yang-Baxter maps, a series of non-autonomous solvable recurrences of order two.