Non-Homogeneous Hydrodynamic Systems and Quasi-Stäckel Hamiltonians - Marciniak, K.; Błaszak, M. (Symmetry, Integrability and Geometry: Methods and Applications, 2017)
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.