On Non-Commutative Integrable Burgers Equations

TL;DR

This paper constructs recursion operators for non-commutative Burgers equations and explores the integrability of mixed versions of these equations using symmetry analysis.

Contribution

It introduces recursion operators for non-commutative Burgers equations and examines the integrability of mixed left- and right-handed versions.

Findings

Recursion operators for non-commutative Burgers equations are constructed.

Existence of integrable mixed Burgers equations is investigated.

Symmetry analysis supports integrability of certain mixed versions.

Abstract

We construct the recursion operators for the non-commutative Burgers equations using their Lax operators. We investigate the existence of any integrable mixed version of left- and right-handed Burgers equations on higher symmetry grounds.