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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Karp's theorem in acoustic scattering theory


Authors: David Colton and Andreas Kirsch
Journal: Proc. Amer. Math. Soc. 103 (1988), 783-788
MSC: Primary 35R30; Secondary 35J05, 35P25, 76Q05
DOI: https://doi.org/10.1090/S0002-9939-1988-0947658-0
MathSciNet review: 947658
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Abstract: Karp's Theorem states that if the far field pattern corresponding to the scattering of a time harmonic plane acoustic wave by a sound-soft cylinder is of the form $ {F_0}(k;\theta - \alpha )$ where $ k$ is the wave number, $ \theta $ the angle of observation and $ \alpha $ the angle of incidence of the plane wave, then the cylinder must be circular. A new proof is given of this result and extended to the cases of scattering by a sound-hard obstacle and an inhomogeneous medium.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0947658-0
Article copyright: © Copyright 1988 American Mathematical Society