Non-Homogeneous Hydrodynamic Systems and Quasi-Stackel Hamiltonians

@article{Marciniak2017NonHomogeneousHS,
  title={Non-Homogeneous Hydrodynamic Systems and Quasi-Stackel Hamiltonians},
  author={Krzysztof Marciniak and Maciej Błaszak},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2017},
  volume={13},
  pages={077}
}
  • K. MarciniakM. Błaszak
  • Published 9 June 2017
  • Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
In this paper we present a novel construction of non-homogeneous hydrodynamic equations from what we call quasi-Stackel systems, that is non-commutatively integrable systems constructed from approp ... 

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References

SHOWING 1-10 OF 22 REFERENCES

Separable Hamiltonians and integrable systems of hydrodynamic type

THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD

It is proved that there exists an infinite involutive family of integrals of hydrodynamic type for diagonal Hamiltonian systems of quasilinear equations; the completeness of the family is also

Classical and Quantum Superintegrability of Stäckel Systems

In this paper we discuss maximal superintegrability of both classical and quantum Stackel systems. We prove a sufficient condition for a flat or constant curvature Stackel system to be maximally su

Commuting quadratic Hamiltonians with velocity dependent potentials

From Stäckel systems to integrable hierarchies of PDE’s: Benenti class of separation relations

We propose a general scheme of constructing of soliton hierarchies from finite dimensional Stackel systems and related separation relations. In particular, we concentrate on the simplest class of

Systematic Construction of Separable Systems with Quadratic in Momenta First Integrals

Liouville integrable separable systems with quadratic in momenta first integrals are considered. Particular attention is paid to the systems generated by the so-called special conformal Killing

Natural coordinates for a class of Benenti systems

On three-dimensional quasi-Stäckel Hamiltonians

A three-dimensional integrable generalization of the Stäckel systems is proposed. A classification of such systems is obtained, which results in two families. The first family is the direct sum of