Fredholm Determinant Solution for the Inverse Scattering Transform of the N x N Zakharov-Shabat Equation

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15 صفحه اول

Inverse Problem and Estimates for Periodic Zakharov-Shabat systems

Consider the Zakharov-Shabat (or Dirac) operator Tzs on L 2(R) L2(R) with real periodic vector potential q = (q1; q2) 2 H = L 2(T) L2(T). The spectrum of Tzs is absolutely continuous and consists of intervals separated by gaps (z n ; z + n ); n 2 Z. >From the Dirichlet eigenvalues mn; n 2 Z of the Zakharov-Shabat equation with Dirichlet boundary conditions at 0; 1, the center of the gap and the...

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It is shown that the inverse scattering problem for the three-dimensional SchrSdinger equation with a potential having no spherical symmetry can be solved using a Fredholm integral equation. The integral operator studied here is shown to be compact and self-adjoint with its spectrum in [-1, 1]. The relationship between solutions of this Fredholm equation and of a related RiemannHilbert problem ...

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ژورنال

عنوان ژورنال: Progress of Theoretical Physics

سال: 1990

ISSN: 0033-068X,1347-4081

DOI: 10.1143/ptp.83.1090