Characterization of the scattering data for the Sturm–Liouville operator. (15th November 2013)

• Record Type: Journal Article
• Authors: Nabiev, A.A.; Saltan, S.; Gürdal, M.
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 17(2014:Nov. 30)
• Page Start: 2626
• Page End: 2637
• Publication Date: 2013-11-15
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3003
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma3003-abs-0001"> <title>Abstract</title> <p id="mma3003-para-0001">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 <italic>q</italic>(<italic>x</italic>) that has different constant asymptotes as <italic>x</italic> → ± ∞ . 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 &amp; Sons, Ltd.</p> </abstract>