Numerical and analytical studies of the discrete nonlinear Schroedinger equation.
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azu_td_9200044_sip1_m.pdf
Author
Schober, Constance Marie.Issue Date
1991Advisor
Ercolani, Nicholas
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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
textDissertation-Reproduction (electronic)
Degree Name
Ph.D.Degree Level
doctoralDegree Program
Applied MathematicsGraduate College