Numerical and analytical studies of the discrete nonlinear Schroedinger equation.

Persistent Link:
http://hdl.handle.net/10150/185595
Title:
Numerical and analytical studies of the discrete nonlinear Schroedinger equation.
Author:
Schober, Constance Marie.
Issue Date:
1991
Publisher:
The University of Arizona.
Rights:
Copyright © 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.
Abstract:
Certain 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.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic; Mathematics; Optics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Ercolani, Nicholas

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleNumerical and analytical studies of the discrete nonlinear Schroedinger equation.en_US
dc.creatorSchober, Constance Marie.en_US
dc.contributor.authorSchober, Constance Marie.en_US
dc.date.issued1991en_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.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.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academicen_US
dc.subjectMathematicsen_US
dc.subjectOptics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorErcolani, Nicholasen_US
dc.contributor.committeememberLevermore, Daviden_US
dc.contributor.committeememberScott, Alwyn C.en_US
dc.contributor.committeememberMcLaughlin, David W.en_US
dc.identifier.proquest9200044en_US
dc.identifier.oclc711786263en_US
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