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

Lakshtanov, Evgeny L.
•
Novikov, Roman G.
•
Vainberg, Boris R.
2016
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ISSN
0049-4704
DOI
e-ISSN
2464-8728
Abstract
We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schroedinger 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.
Series
Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics
48 (2016)
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Publisher
EUT Edizioni Università di Trieste
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