Integral Equations and Operator Theory

, Volume 38, Issue 2, pp 129–171 | Cite as

Direct and inverse scattering for selfadjoint Hamiltonian systems on the line

  • Tuncay Aktosun
  • Martin Klaus
  • Cornelis van der Mee
Article

Abstract

A direct and inverse scattering theory on the full line is developed for a class of first-order selfadjoint 2n×2n systems of differential equations with integrable potential matrices. Various properties of the corresponding scattering matrices including unitarity and canonical Wiener-Hopf factorization are established. The Marchenko integral equations are derived and their unique solvability is proved. The unique recovery of the potential from the solutions of the Marchenko equations is shown. In the case of rational scattering matrices, state space methods are employed to construct the scattering matrix from a reflection coefficient and to recover the potential explicitly.

MSC Primary

34A55 81U40 Secondary 73D50 

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Copyright information

© Birkhäuser Verlag 2000

Authors and Affiliations

  • Tuncay Aktosun
    • 1
  • Martin Klaus
    • 2
  • Cornelis van der Mee
    • 3
  1. 1.Dept. of MathematicsNorth Dakota State Univ.Fargo
  2. 2.Dept. of MathematicsVirginia TechBlacksburg
  3. 3.Dipartimento di MatematicaUniversità di CagliariCagliariItaly

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