Orlov-Schulman symmetries of the self-dual conformal structure equations

TL;DR

This paper constructs and analyzes Orlov-Schulman symmetries within the self-dual conformal structure hierarchy, demonstrating their compatibility with existing flows and illustrating their role via dressing schemes and examples.

Contribution

It introduces explicit constructions of Orlov-Schulman symmetries for SDCS hierarchy and explores their compatibility and representation through dressing schemes.

Findings

Proved compatibility of symmetries with hierarchy flows

Provided explicit examples including Galilean transformations

Presented a dressing scheme interpretation of symmetries

Abstract

We construct Orlov-Schulman symmetries for the self-dual conformal structure (SDCS) hierarchy. We provide an explicit proof of compatibility of additional symmetries with the basic Lax-Sato flows of the hierarchy, and consider several simple examples, including Galilean transformations and scalings. We also present a picture of the Orlov-Schulman symmetries in terms of a dressing scheme based on the Riemann-Hilbert problem.