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Inverse scattering in a layered medium. (English) Zbl 1134.35385
Summary: We study the inverse scattering problem for Schrödinger equation. We prove that for non-smooth potential the main singularities of the potential are contained in the Born approximation which can be obtained from measurement of the scattering amplitude in a single outgoing direction. We measure singularities in the scale of Sobolev spaces.

MSC:
35P25 Scattering theory for PDEs
35L05 Wave equation
35R30 Inverse problems for PDEs
47A40 Scattering theory of linear operators
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