Some remarkableR-separable coordinate systems for the Helmholtz equation |
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| Authors: | E. G. Kalnins W. Miller Jr |
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| Affiliation: | (1) Mathematics Department, University of Waikato, Hamilton, New Zealand;(2) School of Mathematics, University of Minnesota, 55455 Minneapolis, MN, USA |
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| Abstract: | We present examples to show that the phenomenon ofR-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 mayR-separate in more than one way. A satisfactory theory of variable separation for the Helmholtz equation must incorporateR-separation.Supported in part by NSF Grant MCS 78-26216. |
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