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

Abstract

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