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 |