Short-time Asymptotic Analysis of the Manakov System
| dc.contributor.advisor | Ercolani, Nicholas | en_US |
| dc.contributor.advisor | McLaughlin, Kenneth | en_US |
| dc.contributor.author | Espinola Rocha, Jesus Adrian | |
| dc.creator | Espinola Rocha, Jesus Adrian | en_US |
| dc.date.accessioned | 2011-12-06T14:05:11Z | |
| dc.date.available | 2011-12-06T14:05:11Z | |
| dc.date.issued | 2006 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10150/195734 | |
| dc.description.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. | |
| dc.language.iso | EN | en_US |
| dc.publisher | The University of Arizona. | en_US |
| dc.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. | en_US |
| dc.subject | Integrable systems | en_US |
| dc.subject | asymptotic analysis | en_US |
| dc.subject | Solitons | en_US |
| dc.subject | Riemann-Hilbert Problems | en_US |
| dc.subject | Inverse Scattering Transform | en_US |
| dc.subject | Linearized Crank-Nicolson. | en_US |
| dc.title | Short-time Asymptotic Analysis of the Manakov System | en_US |
| dc.type | text | en_US |
| dc.type | Electronic Dissertation | en_US |
| dc.contributor.chair | Ercolani, Nicholas | en_US |
| dc.identifier.oclc | 137356303 | en_US |
| thesis.degree.grantor | University of Arizona | en_US |
| thesis.degree.level | doctoral | en_US |
| dc.contributor.committeemember | McLaughlin, Kenneth | en_US |
| dc.contributor.committeemember | Zakharov, Vladimir | en_US |
| dc.identifier.proquest | 1508 | en_US |
| thesis.degree.discipline | Applied Mathematics | en_US |
| thesis.degree.discipline | Graduate College | en_US |
| thesis.degree.name | PhD | en_US |
| refterms.dateFOA | 2018-06-25T00:39:53Z | |
| html.description.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. |
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