Short-time Asymptotic Analysis of the Manakov System
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azu_etd_1508_sip1_m.pdf
Issue Date
2006Keywords
Integrable systemsasymptotic analysis
Solitons
Riemann-Hilbert Problems
Inverse Scattering Transform
Linearized Crank-Nicolson.
Advisor
Ercolani, NicholasMcLaughlin, Kenneth
Committee Chair
Ercolani, NicholasMetadata
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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
The Manakov system appears in the physics of optical fibers, as well as in quantum mechanics, as multi-component versions of the Nonlinear Schr\"odinger and the Gross-Pitaevskii equations.Although the Manakov system is completely integrable its solutions are far from being explicit in most cases. However, the Inverse Scattering Transform (IST) can be exploited to obtain asymptotic information about solutions.This thesis will describe the IST of the Manakov system, and its asymptotic behavior at short times. I will compare the focusing and defocusing behavior, numerically and analytically, for squared barrier initial potentials. Finally, I will show that the continuous spectrum gives the dominant contribution at short-times.Type
textElectronic Dissertation
Degree Name
PhDDegree Level
doctoralDegree Program
Applied MathematicsGraduate College