Non-Abelian evolution systems with conservation laws

TL;DR

This paper introduces non-Abelian analogs of classical polynomial evolution systems, demonstrating their integrability through explicit zero curvature representations with spectral parameters.

Contribution

It presents the first noncommutative versions of well-known polynomial evolution systems with conservation laws, establishing their integrability.

Findings

Non-Abelian systems with conservation laws are constructed.

Explicit zero curvature representations confirm integrability.

The systems extend classical polynomial evolution models to noncommutative settings.

Abstract

We find noncommutative analogs for well-known polynomial evolution systems with higher conservation laws and symmetries. The integrability of obtained non-Abelian systems is justified by explicit zero curvature representations with spectral parameter.