Non-Homogeneous Hydrodynamic Systems and Quasi-Stäckel Hamiltonians

[摘要] 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.

[关键词] Hamiltonian systems;superintegrable systems;St¨ackel systems;hydrodynamic systems;St¨ackel transform