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Title: A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
Authors: Lakshtanov, Evgeny L.
Novikov, Roman G.
Vainberg, Boris R.
Keywords: two-dimensional inverse scatteringFaddeev functionsgeneralized Riemann-Hilbert-Manakov problemNovikov-Veselov equation
Issue Date: 2016
Publisher: EUT Edizioni Università di Trieste
Series/Report no.: Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics
48 (2016)
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.
Type: Article
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/13150
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.48 (2016)

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