The theory of orthogonal R-separation for Helmholtz equations

E. G. Kalnins; W. Miller

doi:10.1016/0001-8708(84)90004-5

The theory of orthogonal R-separation for Helmholtz equations

E. G. Kalnins, W. Miller

Mathematics

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19 Scopus citations

Abstract

We develop the theory of orthogonal R-separation for the Helmholtz equation on a pseudo-Riemannian manifold and show that it, and not ordinary variable separation, is the natural analogy of additive separation for the Hamiltonian-Jacobi equation. We provide a coordinate-free characterization of R-separation in terms of commuting symmetry operators.

Original language	English (US)
Pages (from-to)	91-106
Number of pages	16
Journal	Advances in Mathematics
Volume	51
Issue number	1
DOIs	https://doi.org/10.1016/0001-8708(84)90004-5
State	Published - Jan 1984

Bibliographical note

Funding Information:
One of us (W.M.) would like to thank the University of Waikato for a Postdoctoral Fellowship and kind hospitality which made this collaboration possible.

Funding Information:
in part by NSF Grant

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abstract = "We develop the theory of orthogonal R-separation for the Helmholtz equation on a pseudo-Riemannian manifold and show that it, and not ordinary variable separation, is the natural analogy of additive separation for the Hamiltonian-Jacobi equation. We provide a coordinate-free characterization of R-separation in terms of commuting symmetry operators.",

author = "Kalnins, {E. G.} and W. Miller",

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N2 - We develop the theory of orthogonal R-separation for the Helmholtz equation on a pseudo-Riemannian manifold and show that it, and not ordinary variable separation, is the natural analogy of additive separation for the Hamiltonian-Jacobi equation. We provide a coordinate-free characterization of R-separation in terms of commuting symmetry operators.

AB - We develop the theory of orthogonal R-separation for the Helmholtz equation on a pseudo-Riemannian manifold and show that it, and not ordinary variable separation, is the natural analogy of additive separation for the Hamiltonian-Jacobi equation. We provide a coordinate-free characterization of R-separation in terms of commuting symmetry operators.

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The theory of orthogonal R-separation for Helmholtz equations

Abstract

Bibliographical note

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