Separable Hamiltonians and integrable systems of hydrodynamic type

DOI10.1016/S0393-0440(96)00013-7zbMath0865.58018MaRDI QIDQ1349440

Evgeny V. Ferapontov, Allan P. Fordy

Publication date: 13 February 1997

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

integrable systemshydrodynamicsseparable Hamiltonians

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) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items

An integrable Hénon–Heiles system on the sphere and the hyperbolic plane, Reciprocal transformations of Hamiltonian operators of hydrodynamic type: Nonlocal Hamiltonian formalism for linearly degenerate systems, An extension of the classical theory of algebraic invariants to pseudo-Riemannian geometry and Hamiltonian mechanics, \(S^{1}\)-equivariant CMC-hypersurfaces in the hyperbolic 3-space and the corresponding Lagrangians, Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems., Non-homogeneous hydrodynamic systems and quasi-Stäckel Hamiltonians, Applications of Nijenhuis geometry. V: Geodesic equivalence and finite-dimensional reductions of integrable quasilinear systems, When a \((1,1)\)-tensor generates separation of variables of a certain metric, Conformal Killing tensors with vanishing torsion and the separation of variables in the Hamilton--Jacobi equation, Unnamed Item, Non-homogeneous systems of hydrodynamic type, related to quadratic Hamiltonians with electromagnetic term, Bi-Hamiltonian separable chains on Riemannian manifolds., On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian., Conformal maps and reductions of the Benney equations, The Gauss-Knörrer map for the Rosochatius dynamical system, Reductions of the Benney equations., Bihamiltonian structures and Stäckel separability, A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems, Curvature as an Integrable Deformation, Commuting quadratic Hamiltonians with velocity dependent potentials, A new construction of recursion operators for systems of hydrodynamic type, From Stäckel systems to integrable hierarchies of PDE’s: Benenti class of separation relations

Cites Work

• Unnamed Item
• Unnamed Item
• The Hénon-Heiles system revisited
• The relationship between Hamiltonian formalisms of stationary and nonstationary problems
• Two remarks about the connection of Jacobi and Neumann integrable systems
• Non-homogeneous systems of hydrodynamic type, related to quadratic Hamiltonians with electromagnetic term
• Reductions of the Benney equations.
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• The Hamiltonian property of an evolutionary flow on the set of stationary points of its integral
• Geodesics on quadrics and a mechanical problem of C. Neumann.
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD