Yang-Baxter maps and matrix solitons

TL;DR

This paper introduces new Yang-Baxter maps derived from the matrix KdV equation, linking integrable systems with set-theoretical solutions to the quantum Yang-Baxter equation.

Contribution

It presents novel Yang-Baxter maps on Grassmannians based on the matrix KdV equation and constructs their Lax pairs via inverse scattering methods.

Findings

New Yang-Baxter maps on Grassmannians are constructed.

Lax pairs for these maps are derived from inverse scattering theory.

The work connects matrix soliton theory with quantum integrable systems.

Abstract

New examples of the Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) on the Grassmannians arising from the theory of the matrix KdV equation are discussed. The Lax pairs for these maps are produced using the relations with the inverse scattering problem for the matrix Schr\"odinger operator.