A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy

Abstract

We develop the Riemann-Hilbert problem approach to in- verse scattering for the two-dimensional Schr odinger equation at xed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and compactly supported poten- tials. In particular, we do not assume that the potential is small or that Faddeev scattering solutions do not have singularities (i.e. we allow the Faddeev exceptional points to exist). Applications of these results to the Novikov-Veselov equation are also considered.