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Lie theory and separation of variables. 9. Orthogonal R-separable coordinate systems for the wave equation psitt−Delta2psi=0
A list of orthogonal coordinate systems which permit R-separation of the wave equation tt−2=0 is presented. All such coordinate systems whose coordinate curves are cyclides or their degenerate f...
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Lie theory and separation of variables. 11. The EPD equation
We show that the Euler–Poisson–Darboux equation {tt−rr−[(2m+1)/r]r}=0 separates in exactly nine coordinate systems corresponding to nine orbits of symmetric second-order operat...

Lie theory and separation of variables. 10. Nonorthogonal R-separable solutions of the wave equation [partial-derivative]ttpsi=Delta2psi

J. Math. Phys. 17, 356 (1976); doi:10.1063/1.522901

Issue Date: March 1976

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E. G. Kalnins
Centre de Recherches Mathématiques, Université de Montréal, Montréal 101, Québec, Canada

W. Miller, Jr.
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
We classify and discuss the possible nonorthogonal coordinate systems which lead to R-separable solutions of the wave equation. Each system is associated with a pair of commuting operators in the symmetry algebra so(3,2) of this equation, one operator first order and the other second order. Several systems appear here for the first time. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
Permalink: http://link.aip.org/link/?JMAPAQ/17/356/1
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PACS

  • 02.20.Qs
    Mathematical methods in physics Group theory General properties, structure, and representation of Lie groups
  • YEAR: 1976

PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
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REFERENCES (14)
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  3. E. G. Kalnins and W. Miller Jr., J. Math. Phys. 15, 1025 (1974).
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  7. C. P. Boyer, E. G. Kalnins, and W. Miller Jr., J. Math. Phys. 16, 512 (1975).
  8. E. G. Kalnins and W. Miller Jr., J. Math. Phys. 17, xxx (1976).
  9. E. G. Kalnins and W. Miller Jr., J. Math. Phys. 17, xxx (1976).
  10. M. Bócher, Ueber die Reihenentwickelungen der Potentialtheorie (Teubner, Leipzig, 1894).
  11. E. G. Kalnins, Ph.D. thesis (University of Western Ontario, 1972).
  12. Ya. I. Azimov, Sov. J. Nucl. Phys. 4, 469 (1967).
  13. E. G. Kalnins, J. Math. Phys. 14, 654 (1973).
  14. A. Bucholz, The Confluent Hypergeometric Function (Springer-Verlag, Berlin, 1969).

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