Browsing by Subject "Jacobi equations"
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Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces
(198308)The Hamilton–Jacobi and Laplace–Beltrami equations on the Hermitian hyperbolic space HH(2) are shown to allow the separation of variables in precisely 12 classes of coordinate systems. The isometry group of this ... 
DifferentialStäckel matrices
(198507)We show that additive separation of variables for linear homogeneous equations of all orders is characterized by differentialStäckel matrices, generalizations of the classical Stäckel matrices used for multiplicative ... 
The general theory of Rseparation for Helmholtz equations
(198305)We develop the theory of Rseparation for the Helmholtz equation on a pseudoRiemannian manifold (including the possibility of null coordinates) and show that it, and not ordinary variable separation, is the natural analogy ... 
Rseparation of variables for the timedependent Hamilton–Jacobi and Schrödinger equations
(198705)The theory of Rseparation of variables is developed for the timedependent Hamilton–Jacobi and Schrödinger equations on a Riemannian manifold V n where timedependent vector and scalar potentials are permitted. As an ... 
Separation of variables on ndimensional Riemannian manifolds. I. The nsphere Sn and Euclidean nspace Rn
(198607)The following problem is solved: What are all the ``different'' separable coordinate systems for the Laplace–Beltrami eigenvalue equation on the nsphere Sn and Euclidean nspace Rn and how are they constructed? This is ...