Characterization of the scattering data for the Sturm-Liouville operator

Characterization of the scattering data for the Sturm-Liouville operator

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 inte...

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Veröffentlicht in:Mathematical methods in the applied sciences 2014-11, Vol.37 (17), p.2626-2637
Hauptverfasser: Nabiev, A.A., Saltan, S., Gürdal, M.
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotes
Coefficients
Constants
Integral equations
integral representation
main integral equation
Mathematical analysis
Operators
Scattering
scattering data
Sturm-Liouville equation
Sturm-Liouville inverse scattering problem
the Jost solution
transformation operator
Work study
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Beschreibung
Zusammenfassung: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3003