Characterization of the scattering data for the Sturm–Liouville operator | Zendy

Nabiev A.A. | Zendy; Saltan S. | Zendy; Gürdal M. | Zendy

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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.

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