Some remarkable R-separable coordinate systems for the Helmholtz equation

E. G. Kalnins; Willard Miller

doi:10.1007/BF00943433

Some remarkable R-separable coordinate systems for the Helmholtz equation

E. G. Kalnins, Willard Miller

School of Mathematics

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6 Scopus citations

Abstract

We present examples to show that the phenomenon of R-separation occurs nontrivially for the Helmholtz equation on a pseudo-Riemannian manifold. R-separable coordinate systems can be both orthogonal and non-orthogonal and a given coordinate system may R-separate in more than one way. A satisfactory theory of variable separation for the Helmholtz equation must incorporate R-separation.

Original language	English (US)
Pages (from-to)	469-474
Number of pages	6
Journal	Letters in Mathematical Physics
Volume	4
Issue number	6
DOIs	https://doi.org/10.1007/BF00943433
State	Published - Nov 1 1980

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title = "Some remarkable R-separable coordinate systems for the Helmholtz equation",

abstract = "We present examples to show that the phenomenon of R-separation occurs nontrivially for the Helmholtz equation on a pseudo-Riemannian manifold. R-separable coordinate systems can be both orthogonal and non-orthogonal and a given coordinate system may R-separate in more than one way. A satisfactory theory of variable separation for the Helmholtz equation must incorporate R-separation.",

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

year = "1980",

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AU - Miller, Willard

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N2 - We present examples to show that the phenomenon of R-separation occurs nontrivially for the Helmholtz equation on a pseudo-Riemannian manifold. R-separable coordinate systems can be both orthogonal and non-orthogonal and a given coordinate system may R-separate in more than one way. A satisfactory theory of variable separation for the Helmholtz equation must incorporate R-separation.

AB - We present examples to show that the phenomenon of R-separation occurs nontrivially for the Helmholtz equation on a pseudo-Riemannian manifold. R-separable coordinate systems can be both orthogonal and non-orthogonal and a given coordinate system may R-separate in more than one way. A satisfactory theory of variable separation for the Helmholtz equation must incorporate R-separation.

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Some remarkable R-separable coordinate systems for the Helmholtz equation

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