Orthogonal separation of variables for the Hamilton-Jacobi and wave equations in three-dimensional Minkowski space

DOI10.1063/1.2823971zbMath1153.81377OpenAlexW1970394077MaRDI QIDQ3544626

Joshua T. Horwood, Raymond G. Mclenaghan

Publication date: 8 December 2008

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

Full work available at URL: https://doi.org/10.1063/1.2823971

Mathematics Subject Classification ID

Wave equation (35L05) Hamilton-Jacobi equations in mechanics (70H20) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Local Riemannian geometry (53B20) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (6)

Classification of the orthogonal separable webs for the Hamilton-Jacobi and Klein-Gordon equations on 3-dimensional Minkowski space ⋮ Equivalence problem for the orthogonal separable webs in 3-dimensional hyperbolic space ⋮ Orthogonal separation of the Hamilton-Jacobi equation on spaces of constant curvature ⋮ Hamilton–Jacobi theory in three-dimensional Minkowski space via Cartan geometry ⋮ On the theory of algebraic invariants of vector spaces of Killing tensors ⋮ Equivalence problem for the orthogonal webs on the 3-sphere

Cites Work

• Unnamed Item
• Unnamed Item
• Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
• Transformation to pseudo-Cartesian coordinates in locally flat pseudo-Riemannian spaces
• Separable systems of Stäckel
• Variable-separation theory for the null Hamilton–Jacobi equation
• Geometrical classification of Killing tensors on bidimensional flat manifolds
• Hamilton–Jacobi theory in three-dimensional Minkowski space via Cartan geometry
• Lie theory and separation of variables. 9. Orthogonal R-separable coordinate systems for the wave equation ψt t−Δ2ψ=0
• Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation
• Group invariant classification of separable Hamiltonian systems in the Euclidean plane and the O(4)-symmetric Yang–Mills theories of Yatsun
• An extension of the classical theory of algebraic invariants to pseudo-Riemannian geometry and Hamiltonian mechanics
• On the Separation of Variables for the Laplace Equation $\Delta \psi + K^2 \psi = 0$ in Two- and Three-Dimensional Minkowski Space
• Intrinsic Characterizations of Orthogonal Separability for Natural Hamiltonians with Scalar Potentials on Pseudo-Riemannian Spaces
• FIXED ENERGY R-SEPARATION FOR SCHRÖDINGER EQUATION
• A geometrical approach to the problem of integrability of Hamiltonian systems by separation of variables

This page was built for publication: Orthogonal separation of variables for the Hamilton-Jacobi and wave equations in three-dimensional Minkowski space