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

DOI10.1063/1.2176908zbMath1111.37039arXivnlin/0511062OpenAlexW3098585374MaRDI QIDQ3441645

Krzysztof Marciniak, Maciej Błaszak

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0511062

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Soliton equations (35Q51)

Related Items (7)

On Reciprocal Equivalence of Stäckel Systems ⋮ Natural coordinates for a class of Benenti systems ⋮ Non-homogeneous hydrodynamic systems and quasi-Stäckel Hamiltonians ⋮ Stäckel representations of stationary KdV systems ⋮ Separability in Riemannian manifolds ⋮ A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems ⋮ Construction of coupled Harry Dym hierarchy and its solutions from Stäckel systems

Cites Work

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• Separable Hamiltonians and integrable systems of hydrodynamic type
• Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems.
• Restricted flows of soliton hierarchies: coupled KdV and Harry Dym case
• Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation
• Separable systems with quadratic in momenta first integrals
• Towards a Theory of Differential Constraints of a Hydrodynamic Hierarchy
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
• Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type
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