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Skew-Self-Adjoint Dirac System with a Rectangular Matrix Potential: Weyl Theory, Direct and Inverse Problems

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Abstract

A non-classical Weyl theory is developed for skew-self-adjoint Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and direct and inverse problems are solved. A Borg–Marchenko type uniqueness result and the evolution of the Weyl function for the corresponding focusing nonlinear Schrödinger equation are also derived.

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Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Mathematisches Institut, Universität Leipzig, Augustusplatz 10/11, 04109, Leipzig, Germany

    B. Fritzsche, B. Kirstein & I. Ya. Roitberg

  2. Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, 1090, Vienna, Austria

    A. L. Sakhnovich

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  1. B. Fritzsche
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  2. B. Kirstein
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  3. I. Ya. Roitberg
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  4. A. L. Sakhnovich
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Correspondence to A. L. Sakhnovich.

Additional information

The work of I. Ya. Roitberg was supported by the German Research Foundation (DFG) under grant no. KI 760/3-1 and the work of A.L. Sakhnovich was supported by the Austrian Science Fund (FWF) under Grant no. Y330.

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Fritzsche, B., Kirstein, B., Roitberg, I.Y. et al. Skew-Self-Adjoint Dirac System with a Rectangular Matrix Potential: Weyl Theory, Direct and Inverse Problems. Integr. Equ. Oper. Theory 74, 163–187 (2012). https://doi.org/10.1007/s00020-012-1997-1

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