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Inverse wave scattering with discontinuous wave speed

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dc.contributorVirginia Techen
dc.contributor.authorAktosun, T.en
dc.contributor.authorKlaus, Martinen
dc.contributor.authorvan der Mee, Cornelisen
dc.contributor.departmentMathematicsen
dc.date.accessed2014-03-20en
dc.date.accessioned2014-04-09T18:12:21Zen
dc.date.available2014-04-09T18:12:21Zen
dc.date.issued1995-06en
dc.description.abstractThe inverse scattering problem on the line is studied for the generalized Schrödinger equation (d 2ψ/dx 2)+k 2 H(x)2ψ=Q(x)ψ, where H(x) is a positive, piecewise continuous function with positive limits H ± as x → ±∞. This equation, in the frequency domain, describes the wave propagation in a nonhomogeneous medium, where Q(x) is the restoring force and 1/H(x) is the variable wave speed changing abruptly at various interfaces. A related Riemann–Hilbert problem is formulated, and the associated singular integral equation is obtained and proved to be uniquely solvable. The solution of this integral equation leads to the recovery of H(x) in terms of the scattering data consisting of Q(x), a reflection coefficient, either of H ±, and the bound state energies and norming constants. Some explicitly solved examples are provided.en
dc.description.sponsorshipNSF DMS-9217627en
dc.description.sponsorshipMURSTen
dc.identifier.citationAktosun, T.; Klaus, M.; Vandermee, C., Inverse wave scattering with discontinuous wave speed," J. Math. Phys. 36, 2880 (1995); http://dx.doi.org/10.1063/1.531338en
dc.identifier.doihttps://doi.org/10.1063/1.531338en
dc.identifier.issn0022-2488en
dc.identifier.urihttp://hdl.handle.net/10919/47053en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/jmp/36/6/10.1063/1.531338en
dc.language.isoen_USen
dc.publisherAIP Publishingen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectnonhomogeneous mediaen
dc.subjectschrodinger-equationen
dc.subjecthilbert problemen
dc.subjectlow-energyen
dc.subjectbehavioren
dc.subjectmatrixen
dc.subjectlineen
dc.titleInverse wave scattering with discontinuous wave speeden
dc.title.serialJournal of Mathematical Physicsen
dc.typeArticle - Refereeden

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