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The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications
The inverse spectral transform for the Zakharov-Shabat equation on the semi-line x>0 is reconsidered as a Hilbert problem. The boundary data induce an essential singularity as k→∞ to one of the basic solutions. Then solving the inverse problem means solving a Hilbert problem with particular prescribed behaviour. It is demonstrated …