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The Zakharov-Shabat Spectral Transform on the Half-line
Auteur(s): Geniet F., Léon J.
(Article) Publié:
Theoretical And Mathematical Physics, vol. 133 p.1504-1515 (2002)
Résumé: 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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