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Some remarkableR-separable coordinate systems for the Helmholtz equation

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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.

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Authors and Affiliations

  1. Mathematics Department, University of Waikato, Hamilton, New Zealand

    E. G. Kalnins

  2. School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA

    W. Miller Jr

Authors
  1. E. G. Kalnins
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  2. W. Miller Jr
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Supported in part by NSF Grant MCS 78-26216.

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Kalnins, E.G., Miller, W. Some remarkableR-separable coordinate systems for the Helmholtz equation. Lett Math Phys 4, 469–474 (1980). https://doi.org/10.1007/BF00943433

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  • DOI: https://doi.org/10.1007/BF00943433

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