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Bäcklund and Darboux transformations for the nonstationary Schrödinger equation

M. Boiti·F. Pempinelli·A. Pogrebkov·B. Prinari
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Abstract

Potentials of the nonstationary Schrödinger operator constructed by means of $n$ recursive Bäcklund transformations are studied in detail. Corresponding Darboux transformations of the Jost solutions are introduced. We show that these solutions obey modified integral equations and present their analyticity properties. Generated transformations of the spectral data are derived.

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M. Boiti, F. Pempinelli, A. Pogrebkov, B. Prinari. 1999-02-16. Bäcklund and Darboux transformations for the nonstationary Schrödinger equation. https://arxiv.org/abs/math-ph/9902019

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