Persistent Link:
http://hdl.handle.net/10150/195734
Title:
Short-time Asymptotic Analysis of the Manakov System
Author:
Espinola Rocha, Jesus Adrian
Issue Date:
2006
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:
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:
text; Electronic Dissertation
Keywords:
Integrable systems; asymptotic analysis; Solitons; Riemann-Hilbert Problems; Inverse Scattering Transform; Linearized Crank-Nicolson.
Degree Name:
PhD
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Ercolani, Nicholas; McLaughlin, Kenneth
Committee Chair:
Ercolani, Nicholas

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleShort-time Asymptotic Analysis of the Manakov Systemen_US
dc.creatorEspinola Rocha, Jesus Adrianen_US
dc.contributor.authorEspinola Rocha, Jesus Adrianen_US
dc.date.issued2006en_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.abstractThe 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.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectIntegrable systemsen_US
dc.subjectasymptotic analysisen_US
dc.subjectSolitonsen_US
dc.subjectRiemann-Hilbert Problemsen_US
dc.subjectInverse Scattering Transformen_US
dc.subjectLinearized Crank-Nicolson.en_US
thesis.degree.namePhDen_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.advisorMcLaughlin, Kennethen_US
dc.contributor.chairErcolani, Nicholasen_US
dc.contributor.committeememberMcLaughlin, Kennethen_US
dc.contributor.committeememberZakharov, Vladimiren_US
dc.identifier.proquest1508en_US
dc.identifier.oclc137356303en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.