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

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.

arXiv admin note: substantial text overlap with arXiv:1106.1263

References in corpus (4)

• Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators
• Sine-Gordon theory in a semi-strip
• Weyl theory and explicit solutions of direct and inverse problems for a Dirac system with rectangular matrix potential
• On the factorization formula for fundamental solutions in the inverse spectral transform

Cited by in corpus (1)

• Weyl functions and the boundary value problem for a matrix nonlinear Schrödinger equation on a semi-strip