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.

References in corpus (3)

• Generalized Stäckel Transform and Reciprocal Transformations for Finite-Dimensional Integrable Systems
• Natural coordinates for a class of Benenti systems
• Classical and Quantum Superintegrability of Stäckel Systems

Cited by in corpus (1)

• Non-autonomous Henon-Heiles system from Painleve class