Integral equation methods for the inverse problem with discontinuous wave speed

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dc.contributor.authorAktosun, Tuncayen
dc.contributor.authorKlaus, Martinen
dc.contributor.authorvan der Mee, Cornelisen
dc.contributor.departmentMathematicsen
dc.date.accessed2014-03-20en
dc.date.accessioned2014-04-09T18:12:20Zen
dc.date.available2014-04-09T18:12:20Zen
dc.date.issued1996-07en
dc.description.abstractThe recovery of the coefficient H(x) in the one-dimensional generalized Schrodinger equation d(2) psi dx(2)+k(2)H(x)(2) psi=Q(x)psi, where H(x) is a positive, piecewise continuous function with positive limits H-+/- as x-->+(+/-infinity), is studied. The large-k asymptotics of the wave functions and the scattering coefficients are analyzed. A factorization formula is given expressing the total scattering matrix as a product of simpler scattering matrices. Using this factorization an algorithm is presented to obtain the discontinuities in H(x) and H'(x)/H(x) in terms of the large-k asymptotics of the reflection coefficient. When there are no bound states, it is shown that H(x) is recovered from an appropriate set of scattering data by using the solution of a singular integral equation, and the unique solvability of this integral equation is established. An equivalent Marchenko integral equation is derived and is shown to be uniquely solvable; the unique recovery of H(x) from the solution of this Marchenko equation is presented. Some explicit examples are given, illustrating the recovery of H(x) from the solution of the singular integral equation and from that of the Marchenko equation. (C) 1996 American Institute of Physics.en
dc.description.sponsorshipNSF DMS-9501053en
dc.description.sponsorshipItalian Ministry of Higher Education and Research (MURST)en
dc.identifier.citationAktosun, T.; Klaus, M.; vanderMee, C., "Integral equation methods for the inverse problem with discontinuous wave speed," J. Math. Phys. 37, 3218 (1996); https://doi.org/10.1063/1.531565en
dc.identifier.doihttps://doi.org/10.1063/1.531565en
dc.identifier.issn0022-2488en
dc.identifier.urihttp://hdl.handle.net/10919/47050en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/jmp/37/7/10.1063/1.531565en
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.subjectscatteringen
dc.titleIntegral equation methods for the inverse problem with discontinuous wave speeden
dc.title.serialJournal of Mathematical Physicsen
dc.typeArticle - Refereeden

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