A Proof of the Soliton Resolution Conjecture for the Focusing Nonlinear Schrödinger Equation
| dc.contributor.advisor | McLaughlin, Kenneth | en |
| dc.contributor.author | Borghese, Michael | |
| dc.creator | Borghese, Michael | en |
| dc.date.accessioned | 2017-06-30T17:05:54Z | |
| dc.date.available | 2017-06-30T17:05:54Z | |
| dc.date.issued | 2017 | |
| dc.identifier.uri | http://hdl.handle.net/10150/624578 | |
| dc.description.abstract | We give a proof of the long-time asymptotic behavior of the focusing nonlinear Schrödinger equation for generic initial condition in which we have simple discrete spectral data and an absence of spectral singularities. The proof relies upon the theory of Riemann-Hilbert problems and the ∂ ̄ method for nonlinear steepest descent. To leading order, the solution will appear as a multi-soliton solution as t → ∞. | |
| dc.language.iso | en_US | en |
| dc.publisher | The University of Arizona. | en |
| 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 |
| dc.title | A Proof of the Soliton Resolution Conjecture for the Focusing Nonlinear Schrödinger Equation | en_US |
| dc.type | text | en |
| dc.type | Electronic Dissertation | en |
| thesis.degree.grantor | University of Arizona | en |
| thesis.degree.level | doctoral | en |
| dc.contributor.committeemember | McLaughlin, Kenneth | en |
| dc.contributor.committeemember | Ercolani, Nicolas | en |
| dc.contributor.committeemember | Kunyansky, Leonid | en |
| dc.contributor.committeemember | Venkataramani, Shankar | en |
| thesis.degree.discipline | Graduate College | en |
| thesis.degree.discipline | Applied Mathematics | en |
| thesis.degree.name | Ph.D. | en |
| refterms.dateFOA | 2018-06-27T17:14:39Z | |
| html.description.abstract | We give a proof of the long-time asymptotic behavior of the focusing nonlinear Schrödinger equation for generic initial condition in which we have simple discrete spectral data and an absence of spectral singularities. The proof relies upon the theory of Riemann-Hilbert problems and the ∂ ̄ method for nonlinear steepest descent. To leading order, the solution will appear as a multi-soliton solution as t → ∞. |
