Generalized dKP: Manakov-Santini hierarchy and its waterbag reduction
  We study Manakov-Santini equation, starting from Lax-Sato form of associated hierarchy. The waterbag reduction for Manakov-Santini hierarchy is introduced. Equations of reduced hierarchy are derived.We construct new coordinates transforming non-hydrodynamic evolution of waterbag reduction to non-homogeneous Riemann invariants form of hydrodynamic type. 
L.V. Bogdanov, Jen-Hsu Chang and Yu-Tung Chen