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

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Export citationKalnins, E. G., & Miller, W., Jr. (1977). Lie theory and the wave equation in space-time. 5. R-separable solutions of the wave equation ψtt-Δ3ψ = 0. Journal of Mathematical Physics, 18(9), 1741–1751. http://doi.org/10.1063/1.523482

Permanent Research Commons link: https://hdl.handle.net/10289/10189

##### Abstract

A detailed classification is made of orthogonal coordinate systems for which the wave equation ψtt - Δ3ψ = 0 admits an R -separable solution. Only those coordinate systems are given which are not conformally equivalent to coordinate systems that have been found in previous articles. We find 106 new coordinates to give a total of 367 conformally inequivalent orthogonal coordinates for which the wave equation admits an R -separation of variables.

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© 1977 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics http://dx.doi.org/10.1063/1.523482