The Orlov–Schulman Symmetries of the Manakov–Santini Hierarchy

Key Points

• The aim is to construct Orlov–Schulman symmetries within the Manakov–Santini hierarchy and examine their properties.
• Constructed symmetries of the Manakov–Santini hierarchy.
• Provided explicit proof of compatibility with hierarchy flows.
• Explored examples including Galilean transformations and scalings.
• Utilized the dressing scheme related to the Riemann–Hilbert problem.
• Demonstrated compatibility of additional symmetries with fundamental flows.
• Illustrated the presence of various symmetries in the context of simple transformations.
• Provided a framework for understanding symmetries through a dressing scheme.