Title: Non-Homogeneous Hydrodynamic Systems and Quasi-Stäckel Hamiltonians,
Abstract: In this paper we present a novel construction of non-homogeneous hydrodynamic
equations from what we call quasi-Stäckel systems, that is non-commutatively
integrable systems constructed from appropriate maximally superintegrable
Stäckel systems. We describe the relations between Poisson algebras generated
by quasi-Stäckel Hamiltonians and the corresponding Lie algebras of vector
fields of non-homogeneous hydrodynamic systems. We also apply Stäckel
transform to obtain new non-homogeneous equations of considered type.