Abstract
The Zakharov–Shabat inverse spectral problem is constructed for a potential with support on the half-line and with a boundary value at the origin. This prescribed value is shown to produce a Jost solution with an essential singularity at large values of the spectral parameter; this requires particular attention when solving the related Hilbert boundary value problem. The method is then used to illustrate the sine-Gordon equation (in the light cone) and is discussed using a singular limit of the stimulated Raman scattering equations.
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Geniet, F., Leon, J. Zakharov–Shabat Spectral Transform on the Half-Line. Theoretical and Mathematical Physics 133, 1504–1515 (2002). https://doi.org/10.1023/A:1021194610240
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DOI: https://doi.org/10.1023/A:1021194610240