RECONSTRUCTION OF SINGULARITIES OF A SCATTERING POTENTIAL IN 2 DIMENSIONS

In this paper, we consider the inverse scattering problem for the Schr odinger equation in two dimensions. This problem of reconstructing the scattering potential from the far field data has a well-known approxi mate solution based on the linearization through the weak scatterer (o r Born) approximation. In the present work it is shown that while this approximate solution need not be close to the underlying scattering p otential, the leading local singularities of the potential are recover ed exactly in this procedure. (C) 1994 Academic Press, Inc.