Variable-separation theory for the null Hamilton–Jacobi equation

DOI10.1063/1.1862325zbMath1067.70017OpenAlexW1974490605MaRDI QIDQ3024312

Giovanni Rastelli, C. Chanu, Sergio Benenti

Publication date: 30 June 2005

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

Full work available at URL: https://doi.org/10.1063/1.1862325

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Hamilton-Jacobi equations in mechanics (70H20) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

Related Items (14)

Nonstandard Separability on the Minkowski Plane ⋮ Energy dependent integrability ⋮ Conformal killing tensors and covariant Hamiltonian dynamics ⋮ Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion ⋮ ( 1 + 1 ) -dimensional separation of variables ⋮ Invariant classification of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space ⋮ Orthogonal separation of variables for the Hamilton-Jacobi and wave equations in three-dimensional Minkowski space ⋮ Polynomial separable indefinite natural systems ⋮ Symmetry operators and separation of variables for Dirac's equation on two-dimensional spin manifolds with external fields ⋮ Superintegrable three-body systems on the line ⋮ \(R\)-separation of variables for the conformally invariant Laplace-Beltrami equation ⋮ FIXED ENERGY R-SEPARATION FOR SCHRÖDINGER EQUATION ⋮ The anisotropic Calderón problem on 3-dimensional conformally Stäckel manifolds ⋮ Separability and symmetry operators for Painlevé metrics and their conformal deformations

Cites Work

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• Remarks on the connection between the additive separation of the Hamilton–Jacobi equation and the multiplicative separation of the Schrödinger equation. I. The completeness and Robertson conditions
• Invariants at fixed and arbitrary energy. A unified geometric approach
• The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body

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