on the Riemann-Hilbert problem for the one-dimensional Schrodinger-equation
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A matrix Riemann-Hilbert problem associated with the one-dimensional Schrodinger equation is considered, and the existence and uniqueness of its solutions are studied. The solution of this Riemann-Hilbert problem yields the solution of the inverse scattering problem for a larger class of potentials than the usual Faddeev class. Some examples of explicit solutions of the Riemann-Hilbert problem are given, and the connection with ambiguities in the inverse scattering problem is established.