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

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.