**Valery Serov
University of Oulu and UW**

*Date:* February 13, 2006

This work deals with the inverse scattering problem for
two-dimensional Schroedinger operator. The following problem is
studied: To estimate more accurately first nonlinear term from the
Born's series which corresponds to the scattering data with all
arbitrary large energies and all angles in the scattering
amplitude. This estimate allows us to conclude that all singularities
and jumps of the unknown potential can be obtained exactly by the Born
approximation. Especially, for the potentials from -spaces the
approximation agrees with the true potential up to the continuous
function. Generalizations for higher dimensions are considered as
well as other inverse scattering problems.