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Symmetry and separation of variables for the Helmholtz and Laplace equations

Published online by Cambridge University Press:  22 January 2016

C. P. Boyer
Affiliation:
Universidad Nacional Autonoma de Mexico
E. G. Kalnins
Affiliation:
University of Waikato
W. Miller
Affiliation:
University of Minnesota
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Extract

This paper is one of a series relating the symmetry groups of the principal linear partial differential equations of mathematical physics and the coordinate systems in which variables separate for these equations. In particular, we mention [1] and paper [2] which is a survey of and introduction to the series. Here we apply group-theoretic methods to study the separable coordinate systems for the Helmholtz equation.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Boyer, C., Kalnins, E. G., and Miller, W. Jr., Lie theory and separation of variables. 6. The equation iUt + Δ2U=0 , J. Math. Phys., 16 (1975), 499511.CrossRefGoogle Scholar
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[11] Erdélyi, A. et al., Higher Transcendental Functions. Vols. 1 and 2, McGraw-Hill, New York, 1953.Google Scholar
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