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Journal of the Physical Society of Japan, September 15, 1984, Vol. 53, No. 9 : pp. 2879-2884 2×2-Matrix Riemann-Hilbert Transform and Its Connection to the Continuous Scattering Data Tsutomu Kawata https://doi.org/10.1143/JPSJ.53.2879

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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.

https://doi.org/10.1143/JPSJ.53.2879

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