A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
Mathematical Physics
2016-12-19 v1 Analysis of PDEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schrodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and compactly supported potentials. 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.
Cite
@article{arxiv.1509.06495,
title = {A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy},
author = {Evgeny L. Lakshtanov and Roman G. Novikov and Boris R. Vainberg},
journal= {arXiv preprint arXiv:1509.06495},
year = {2016}
}