Integral Equations and Operator Theory

, Volume 30, Issue 3, pp 279–316

Inverse scattering in one-dimensional nonconservative media

  • Tuncay Aktosun
  • Martin Klaus
  • Cornelis van der Mee

DOI: 10.1007/BF01195585

Cite this article as:
Aktosun, T., Klaus, M. & van der Mee, C. Integr equ oper theory (1998) 30: 279. doi:10.1007/BF01195585


The inverse scattering problem arising in wave propagation in one-dimensional non-conservative media is analyzed. This is done in the frequency domain by considering the Schrödinger equation with the potentialikP(x)+Q(x), wherek2 is the energy andP(x) andQ(x) are real integrable functions. Using a pair of uncoupled Marchenko integral equations,P(x) andQ(x) are recovered from an appropriate set of scattering data including bound-state information. Some illustrative examples are provided.

MSC Primary

34A55 81U40 Secondary 73D50 

Copyright information

© Birkhäuser Verlag 1998

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 Polytechnic Inst. and State Univ.Blacksburg
  3. 3.Dipartimento di MatematicaUniversità di CagliariCagliariItaly

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