2×2-Matrix Riemann-Hilbert Transform and Its Connection to the Continuous Scattering Data

  • Kawata Tsutomu
    Department of Information Processing, Faculty of Engineering, Toyama University

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  • 2 2 Matrix Riemann Hilbert Transform an

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A basic 2×2-matrix Riemann-Hilbert problem is studied and its complete connection to the associated eigenvalue problem is made clear. A potential formula independent on the spectral parameter λ is derived by considering a transformation contributed from the continuous data. As a by-product we get a mapping from the variation of scattering data to the one of potentials.

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