Riemann-Hilbert factorizations and inverse scattering for the AKNS- equation with \(L^ 1\)-potentials. I (Q1322399)
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scientific article; zbMATH DE number 562832
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Riemann-Hilbert factorizations and inverse scattering for the AKNS- equation with \(L^ 1\)-potentials. I |
scientific article; zbMATH DE number 562832 |
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Riemann-Hilbert factorizations and inverse scattering for the AKNS- equation with \(L^ 1\)-potentials. I (English)
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5 May 1994
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Summary: A detailed group theoretic approach is developed for the \(2 \times 2\) AKNS system with potentials supported on the half-line. This approach uses consistently Riemann-Hilbert splittings interpreted as factorizations in certain Banach Lie groups. In particular, it is shown how meromorphic splittings introduced by Beals and Coifman can be replaced with regular Riemann-Hilbert splittings leading to the group theoretic notion of a scattering data.
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Riemann-Hilbert splitting
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Banach Lie groups
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scattering map
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