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Zakharov–Shabat Spectral Transform on the Half-Line
F. Geniet, G. Leon Universite Montpellier II
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.
Keywords:
nonlinear evolution equations, inverse scattering transform, boundary value problem, Riemann–Hilbert problem, sine-Gordon equation.
Citation:
F. Geniet, G. Leon, “Zakharov–Shabat Spectral Transform on the Half-Line”, TMF, 133:2 (2002), 218–232; Theoret. and Math. Phys., 133:2 (2002), 1504–1515
Linking options:
https://www.mathnet.ru/eng/tmf392https://doi.org/10.4213/tmf392 https://www.mathnet.ru/eng/tmf/v133/i2/p218
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