2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229360We 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.16 pagesExactly Solvable and Integrable Systemstext