Geodesic
Zakharov--Shabat Spectral Transform on the Half-Line
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 218-232

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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.
Keywords: nonlinear evolution equations, inverse scattering transform, boundary value problem, Riemann–Hilbert problem
Mots-clés : sine-Gordon equation. 
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     author = {F. Geniet and G. Leon},
     title = {Zakharov--Shabat {Spectral} {Transform} on the {Half-Line}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a7/}
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F. Geniet; G. Leon. Zakharov--Shabat Spectral Transform on the Half-Line. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 2, pp. 218-232. http://geodesic.mathdoc.fr/item/TMF_2002_133_2_a7/