On the inverse problem of the scattering theory for a boundary value problem. (English) Zbl 1106.34059

Menken, Hamza; Mamedov, Khanlar R.

Mladenov, Ivaïlo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2–10, 2005. Sofia: Bulgarian Academy of Sciences (ISBN 954-8495-30-9/pbk). 226-236 (2006).

Following the lines of the Gelfand-Levitan-Marchenko theory, the authors solve an inverse scattering problem for the (one-dimensional) Schrödinger equation on the half-line with a boundary condition at 0, which depends linearly on the spectral parameter.
For the entire collection see [Zbl 1089.53004].

Reviewer: Vassilis G. Papanicolaou (Athena)

MSC:

34L25	Scattering theory, inverse scattering involving ordinary differential operators
34B40	Boundary value problems on infinite intervals for ordinary differential equations
34L40	Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)

Keywords:

Schrödinger equation on the half-line; inverse scattering problem; scattering data; Gelfand-Levitan-Marchenko theory; boundary condition containing the spectral parameter