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Inverse scattering problem for Sturm–Liouville operator with nonlinear dependence on the spectral parameter in the boundary condition
Author(s) -
Mamedov Kh. R.,
Kosar N. P.
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1352
Subject(s) - mathematics , inverse scattering transform , inverse scattering problem , mathematical analysis , uniqueness , boundary value problem , sturm–liouville theory , scattering , operator (biology) , quantum inverse scattering method , inverse problem , quadratic equation , scattering theory , nonlinear system , boundary (topology) , physics , quantum mechanics , geometry , biochemistry , chemistry , repressor , transcription factor , gene
The inverse problem of the scattering theory for Sturm–Liouville operator on the half line with boundary condition depending quadratic on the spectral parameter is considered. Scattering data are defined, some properties of the scattering data are examined, the main equation is obtained, solvability of the integral equation is proved and uniqueness of algorithm to the potential with given scattering data is studied. Copyright © 2010 John Wiley & Sons, Ltd.