Orlov–Schulman symmetries of multidimensional dispersionless integrable hierarchies

Abstract: We construct Orlov-Schulman symmetries for multidimensional dispersionless integrable hierarchies, focusing on illustrative examples of the (2+1)-dimensional Manakov-Santini (MS) hierarchy and (2+2)-dimensional 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 of the symmetries, including Galilean transformations and scalings. We also present a description of Orlov-Schulman symmetries in terms of a dressing scheme based on the Riemann-Hilbert problem.

Paper links: arXiv:2509.19923, arXiv:2604.19282

mathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

Geometry of differential equations seminar