Persistent Link:
http://hdl.handle.net/10150/282547
Title:
THE INITIAL-VALUE PROBLEM FOR ZERO AREA PULSES
Author:
Shakir, Sami Ali
Issue Date:
1980
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 purpose of this work is to study the initial value problem for coherent pulse propagation (SIT) for zero area pulses. We employ the machinery of the newly developed mathematical technique of the inverse scattering method (ISM) to deduce general rules by which one can predict the kind of output pulses for a given input pulse impinging on a resonant attenuator. This study is relevant since the area theorem cannot provide unambiguous information about zero area pulses. Thus in effect we introduce an equivalent and more general formulation to the theorem in terms of the reflection coefficient, r(ν), of the ISM. The poles of r(ν) correspond to the steady state solitary pulses called solitons. We show that the threshold for soliton generation, including breathers, is for an absolute initial area of about π, a result consistent with the predictions of the area theorem. We solve an example of an input zero area profile. We also show that if the input pulse has an odd profile with respect to time, only breathers can be expected as solitons. We demonstrate that the conservation equations are of limited use when applied to zero area pulses. They give satisfactory results only in a limited region. We compare the predictions of the conservation equations to the predictions of the ISM, and come to the conclusion that for zero area pulses, the ISM is the only known satisfactory approach.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Laser pulses, Ultrashort.; Solitons.; Eigenvalues.; Scattering (Mathematics)
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Optical Sciences
Degree Grantor:
University of Arizona
Advisor:
Hopf, Fred

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleTHE INITIAL-VALUE PROBLEM FOR ZERO AREA PULSESen_US
dc.creatorShakir, Sami Alien_US
dc.contributor.authorShakir, Sami Alien_US
dc.date.issued1980en_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 purpose of this work is to study the initial value problem for coherent pulse propagation (SIT) for zero area pulses. We employ the machinery of the newly developed mathematical technique of the inverse scattering method (ISM) to deduce general rules by which one can predict the kind of output pulses for a given input pulse impinging on a resonant attenuator. This study is relevant since the area theorem cannot provide unambiguous information about zero area pulses. Thus in effect we introduce an equivalent and more general formulation to the theorem in terms of the reflection coefficient, r(ν), of the ISM. The poles of r(ν) correspond to the steady state solitary pulses called solitons. We show that the threshold for soliton generation, including breathers, is for an absolute initial area of about π, a result consistent with the predictions of the area theorem. We solve an example of an input zero area profile. We also show that if the input pulse has an odd profile with respect to time, only breathers can be expected as solitons. We demonstrate that the conservation equations are of limited use when applied to zero area pulses. They give satisfactory results only in a limited region. We compare the predictions of the conservation equations to the predictions of the ISM, and come to the conclusion that for zero area pulses, the ISM is the only known satisfactory approach.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectLaser pulses, Ultrashort.en_US
dc.subjectSolitons.en_US
dc.subjectEigenvalues.en_US
dc.subjectScattering (Mathematics)en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineOptical Sciencesen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorHopf, Freden_US
dc.identifier.proquest8027746en_US
dc.identifier.oclc8633103en_US
dc.identifier.bibrecord.b18059181en_US
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