Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 077, 15 pages      arXiv:1706.02873      https://doi.org/10.3842/SIGMA.2017.077

Non-Homogeneous Hydrodynamic Systems and Quasi-Stäckel Hamiltonians

Krzysztof Marciniak a and Maciej Błaszak b
a) Department of Science and Technology, Campus Norrköping, Linköping University, Sweden
b) Faculty of Physics, Division of Mathematical Physics, A. Mickiewicz University, Poznań, Poland

Received June 12, 2017, in final form September 25, 2017; Published online September 28, 2017

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.

Key words: Hamiltonian systems; superintegrable systems; Stäckel systems; hydrodynamic systems; Stäckel transform.

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