Skew-self-adjoint Dirac systems with a rectangular matrix potential: Weyl theory, direct and inverse problems

2011/12/04 by B. Fritzsche, B. Kirstein, I. Ya. Roitberg +1 · 1 citation
Mathematics · Physics and Astronomy · #math.CA #math-ph #math.MP #math.SP #nlin.SI #msc:34B20 #msc:34L40 #msc:37K15

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published as Integral Equations and Operator Theory, 74:2 (2012), 163--187 · arXiv admin note: substantial text overlap with arXiv:1106.1263

arxiv created 2011/12/04 · arxiv updated 2012/11/29

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.

Cited by

• Evolution of Weyl functions and initial-boundary value problems
• Asymptotics of Titchmarsh--Weyl functions near the real axis andan application to the KdV hierarchy

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