Karp’s theorem in acoustic scattering theory

Colton, David; Kirsch, Andreas

doi:10.1090/S0002-9939-1988-0947658-0

Karp’s theorem in acoustic scattering theory
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by David Colton and Andreas Kirsch PDF

Proc. Amer. Math. Soc. 103 (1988), 783-788 Request permission

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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Higher transcendental Functions

The two dimensional inverse scattering problem

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