Dressing Method for The Schrodinger Eigenvalue Problem

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  • シュレディンガー コユウチ モンダイ ノ ドレッシングホウ エイブン
  • シュレデインガー固有値問題のドレッシング法

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The Riemann-Hilbert problem (RHP) plays a key role on the invers scattering transform (IST), by which many types of nonlinear evolution equations (NLEE's) can be solved. The IST of Schrodinger cperator is reviewed in some content, that is, a vector formalism is given. Considerations of the reviews enabled us to derive the dressing method (originally developed by Zakharov and Shabat) which is also powerful to solve the NLEE's. Connections between both methods are made clear. We find that a Schrodinger problem results in the dressing method and the Gel'fand-Levitan type of integral equations (GLE) is also derived with the same spectral function as the one of the 1ST. This fact means to define the scattering data still for the dressing method.

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