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Integral Equations and Operator Theory

, Volume 84, Issue 3, pp 323–355 | Cite as

Inverse Scattering on the Half-Line for ZS-AKNS Systems with Integrable Potentials

  • Rostyslav O. Hryniv
  • Stepan S. Manko
Open Access
Article

Abstract

In this paper, we study the inverse scattering problem for ZS-AKNS systems on the half-line with general boundary conditions at the origin. For the class of potentials with certain integrability properties, we give a complete description of the corresponding scattering functions S, justify the algorithm reconstructing the potential and the boundary conditions from S, and prove that the scattering map is homeomorphic.

Keywords

Inverse problems ZS-AKNS systems Scattering function 

Mathematics Subject Classification

Primary 34L25 Secondary 34L40 81U20 81U40 

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Authors and Affiliations

  1. 1.Institute for Applied Problems of Mechanics and MathematicsLvivUkraine
  2. 2.Faculty of Mathematics and Natural SciencesUniversity of RzeszówRzeszówPoland
  3. 3.Doppler Institute for Mathematical Physics and Applied MathematicsCzech Technical University in PraguePragueCzech Republic
  4. 4.Department of Physics, Faculty of Nuclear Science and Physical EngineeringCzech Technical University in PragueDěčínCzech Republic

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