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dc.contributor.advisorErcolani, Nicholasen_US
dc.contributor.authorSchober, Constance Marie.
dc.creatorSchober, Constance Marie.en_US
dc.date.accessioned2011-10-31T17:42:40Z
dc.date.available2011-10-31T17:42:40Z
dc.date.issued1991en_US
dc.identifier.urihttp://hdl.handle.net/10150/185595
dc.description.abstractCertain conservative discretizations of the Nonlinear Schroedinger (NLS) Equation can produce irregular behavior. We consider the diagonal discretization as a conservative perturbation of the integrable discretization and study the homoclinic crossings in its nonlinear spectrum. We find that irregularity sets in for the two unstable mode regime and, in this case, many and continual homoclinic crossings occur throughout the irregular time series. We undertake an analysis to determine the mechanism that causes the "chaotic" behavior to appear in this conservatively perturbed NLS equation. This analysis involves the construction of explicit formulas for the homoclinic orbit, a description of the relevant finite dimensional phase space and a Melnikov analysis for the various regimes studied.
dc.language.isoenen_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.subjectDissertations, Academicen_US
dc.subjectMathematicsen_US
dc.subjectOptics.en_US
dc.titleNumerical and analytical studies of the discrete nonlinear Schroedinger equation.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.identifier.oclc711786263en_US
thesis.degree.grantorUniversity of Arizonaen_US
thesis.degree.leveldoctoralen_US
dc.contributor.committeememberLevermore, Daviden_US
dc.contributor.committeememberScott, Alwyn C.en_US
dc.contributor.committeememberMcLaughlin, David W.en_US
dc.identifier.proquest9200044en_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.namePh.D.en_US
refterms.dateFOA2018-08-13T22:40:26Z
html.description.abstractCertain conservative discretizations of the Nonlinear Schroedinger (NLS) Equation can produce irregular behavior. We consider the diagonal discretization as a conservative perturbation of the integrable discretization and study the homoclinic crossings in its nonlinear spectrum. We find that irregularity sets in for the two unstable mode regime and, in this case, many and continual homoclinic crossings occur throughout the irregular time series. We undertake an analysis to determine the mechanism that causes the "chaotic" behavior to appear in this conservatively perturbed NLS equation. This analysis involves the construction of explicit formulas for the homoclinic orbit, a description of the relevant finite dimensional phase space and a Melnikov analysis for the various regimes studied.


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