The semiclassical limit of the defocusing nonlinear Schroedinger flows.

Persistent Link:
http://hdl.handle.net/10150/185687
Title:
The semiclassical limit of the defocusing nonlinear Schroedinger flows.
Author:
Jin, Shan.
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:
The Lax-Levermore strategy for analyzing the zero-dispersion limit of the KdV equation through its inverse scattering transform can be adapted to study the semiclassical limits of the defocusing nonlinear Schrodinger (NLS) equation, which are in fact the limits of corresponding conservation laws. The weak limits of all conserved densities and their fluxes can be characterized in terms of the solution of a variational problem that in turn can be solved using function theory. These results rest on a new formula for the N-soliton solutions and a WKB analysis of the semiclassical limit for the direct and inverse Zakharov-Shabat scattering transform. Moreover, with Levermore's method, one can see that the limiting dynamics explored is hyperbolic and agrees with that obtained by classical nonlinear modulation theory. The result is extended to the whole NLS hierarchy.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic; Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Levermore, C. David

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleThe semiclassical limit of the defocusing nonlinear Schroedinger flows.en_US
dc.creatorJin, Shan.en_US
dc.contributor.authorJin, Shan.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.abstractThe Lax-Levermore strategy for analyzing the zero-dispersion limit of the KdV equation through its inverse scattering transform can be adapted to study the semiclassical limits of the defocusing nonlinear Schrodinger (NLS) equation, which are in fact the limits of corresponding conservation laws. The weak limits of all conserved densities and their fluxes can be characterized in terms of the solution of a variational problem that in turn can be solved using function theory. These results rest on a new formula for the N-soliton solutions and a WKB analysis of the semiclassical limit for the direct and inverse Zakharov-Shabat scattering transform. Moreover, with Levermore's method, one can see that the limiting dynamics explored is hyperbolic and agrees with that obtained by classical nonlinear modulation theory. The result is extended to the whole NLS hierarchy.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academicen_US
dc.subjectMathematics.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.advisorLevermore, C. Daviden_US
dc.contributor.committeememberMcLaughlin, David W.en_US
dc.contributor.committeememberErcolani, Nicken_US
dc.contributor.committeememberFaris, William G.en_US
dc.contributor.committeememberFlaschka, Hermannen_US
dc.contributor.committeememberGreenlee, Martinen_US
dc.identifier.proquest9210294en_US
dc.identifier.oclc711906436en_US
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