Lie theory and the wave equation in space-time. 5. R-separable solutions of the wave equation ψtt - Δ3ψ = 0

E. G. Kalnins; W. Miller

doi:10.1063/1.523820

Lie theory and the wave equation in space-time. 5. R-separable solutions of the wave equation ψ_tt - Δ₃ψ = 0

E. G. Kalnins, W. Miller

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Abstract

A detailed classification is made of all orthogonal coordinate systems for which the wave equation ψ - Δ₃ψ = 0 admits an R-separable solution. Only those coordinate systems are given which are not conformally equivalent to coordinate systems that have already been found in previous articles. We find 106 coordinates to given a total of 368 conformally inequivalent orthogonal coordinates for which the wave equation admits an R separation of variables.

Original language	English (US)
Pages (from-to)	1247-1257
Number of pages	11
Journal	Journal of Mathematical Physics
Volume	19
Issue number	6
DOIs	https://doi.org/10.1063/1.523820
State	Published - 1977
Externally published	Yes

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10.1063/1.523820

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abstract = "A detailed classification is made of all orthogonal coordinate systems for which the wave equation ψ - Δ3ψ = 0 admits an R-separable solution. Only those coordinate systems are given which are not conformally equivalent to coordinate systems that have already been found in previous articles. We find 106 coordinates to given a total of 368 conformally inequivalent orthogonal coordinates for which the wave equation admits an R separation of variables.",

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

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N2 - A detailed classification is made of all orthogonal coordinate systems for which the wave equation ψ - Δ3ψ = 0 admits an R-separable solution. Only those coordinate systems are given which are not conformally equivalent to coordinate systems that have already been found in previous articles. We find 106 coordinates to given a total of 368 conformally inequivalent orthogonal coordinates for which the wave equation admits an R separation of variables.

AB - A detailed classification is made of all orthogonal coordinate systems for which the wave equation ψ - Δ3ψ = 0 admits an R-separable solution. Only those coordinate systems are given which are not conformally equivalent to coordinate systems that have already been found in previous articles. We find 106 coordinates to given a total of 368 conformally inequivalent orthogonal coordinates for which the wave equation admits an R separation of variables.

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Lie theory and the wave equation in space-time. 5. R-separable solutions of the wave equation ψ_tt - Δ₃ψ = 0

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