On the Eigenvalues of the Manakov System

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dc.contributor.authorKeister, Adrian Clarken
dc.contributor.committeechairKlaus, Martinen
dc.contributor.committeememberDay, Martin V.en
dc.contributor.committeememberKohler, Werner E.en
dc.contributor.committeememberJacobs, Iraen
dc.contributor.committeememberHagedorn, George A.en
dc.contributor.departmentMathematical Physicsen
dc.date.accessioned2014-03-14T20:13:37Zen
dc.date.adate2007-07-13en
dc.date.available2014-03-14T20:13:37Zen
dc.date.issued2007-06-26en
dc.date.rdate2007-07-13en
dc.date.sdate2007-06-30en
dc.description.abstractWe clear up two issues regarding the eigenvalue problem for the Manakov system; these problems relate directly to the existence of the soliton [sic] effect in fiber optic cables. The first issue is a bound on the eigenvalues of the Manakov system: if the parameter ξ is an eigenvalue, then it must lie in a certain region in the complex plane. The second issue has to do with a chirped Manakov system. We show that if a system is chirped too much, the soliton effect disappears. While this has been known for some time experimentally, there has not yet been a theoretical result along these lines for the Manakov system.en
dc.description.degreePh. D.en
dc.identifier.otheretd-06302007-091322en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06302007-091322/en
dc.identifier.urihttp://hdl.handle.net/10919/28169en
dc.publisherVirginia Techen
dc.relation.haspartFinalDraft.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectZakharov-Shabaten
dc.subjectchirpen
dc.subjectfiber opticsen
dc.subjectinverse scattering transformen
dc.subjectsolitonen
dc.subjectcoupled nonlinear Schrödinger equationsen
dc.subjectnonlinear Schrödinger equationen
dc.subjectManakoven
dc.titleOn the Eigenvalues of the Manakov Systemen
dc.typeDissertationen
thesis.degree.disciplineMathematical Physicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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