Lie theory and the wave equation in space–time. 5. R-separable solutions of the wave equation ψt t−Δ3ψ=0

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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.