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- W2020668832 abstract "The Marchenko equation for the N ×N Zakharov-Shabat operator on the line is given via the Riemann-Hilbert problem. It is derived on the basis of the direct spectral problem which was solved through the Fredholm integral equation. In the 2 ×2 problem the Marchenko equations for the right and the left inverse problems are separated but in the N ×N case we obtain a coupled Marchenko equations. The integral kernel of the Marchenko equation is shown to be of the Hilbert-Schmidt type for a general class of Schwarz type potentials and hence in the inverse problem the equation is solvable by the theorem of the Fredholm alternatives. Finally reduction to the 2 ×2 case is briefly discussed." @default.
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- W2020668832 date "1988-11-01" @default.
- W2020668832 modified "2023-10-14" @default.
- W2020668832 title "The Marchenko Equation of the Hilbert-Schmidt Type for the N xN Zakharov-Shabat Operator" @default.
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- W2020668832 doi "https://doi.org/10.1143/ptp.80.774" @default.
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