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

Research output: Contribution to journal › Article

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

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title = "The theory of orthogonal R-separation for Helmholtz equations",

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.",

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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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