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Multi-valued solutions of the wave equation

Published online by Cambridge University Press:  24 October 2008

F. G. Friedlander
F. G. Friedlander
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Extract

It was first pointed out by Sommerfeld, around the turn of the century, that certain multi-valued solutions of the wave equation in ℝ3 can be used to deal with the problem of scattering by a wedge, or reflection in a corner. The older literature on this subject is extensive; see ((4), chapter 5) for references up to 1958. The object of this Note is to give an explicit and elementary construction of a forward fundamental solution of the wave equation, of this type, in ℝn+1, where n ≥ 2; for n = 2 this includes Sommer-feld's original result.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 2 , September 1981 , pp. 335 - 341
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Cheeger, J. and Taylor, M. On the diffraction of waves by conical singularities. (To be published).Google Scholar
(2)Friedlander, F. G.A singular initial-boundary value problem for a generalized Euler-Darboux equation. J. Diff. Equ. (in the Press).Google Scholar
(3)Friedlander, F. G.The wave equation on a curved space-time (Cambridge University Press, 1975).Google Scholar
(4)Friedlander, F. G.Sound pulses (Cambridge University Press, 1958).Google Scholar
(5)Thompson, Jon H.Closed solutions for wedge diffraction. SIAM J. Appl. Math. 22 (1972), 300–306.CrossRefGoogle Scholar