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Characterization of the scattering data for the Sturm–Liouville operator
Author(s) -
Nabiev A.A.,
Saltan S.,
Gürdal M.
Publication year - 2013
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.3003
Subject(s) - asymptote , scattering , mathematics , mathematical analysis , constant (computer programming) , operator (biology) , sturm–liouville theory , inverse scattering problem , scattering theory , inverse scattering transform , integral equation , characterization (materials science) , inverse problem , physics , optics , boundary value problem , chemistry , computer science , biochemistry , repressor , transcription factor , gene , programming language
This work studies the scattering problem on the real axis for the Sturm–Liouville equation with discontinuous leading coefficient and the real‐valued steplike potential q ( x ) that has different constant asymptotes as x → ± ∞ . We investigate the properties of the scattering data, obtain the main integral equations of the inverse scattering problem, and also give necessary and sufficient conditions characterizing the scattering data. Copyright © 2013 John Wiley & Sons, Ltd.