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

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.