Nonlinear Schrödinger systems on the three-dimensional torus
| dc.contributor.advisor | Chen, Thomas (Ph. D. in mechanical engineering and Ph. D. in mathematical physics) | |
| dc.contributor.committeeMember | Pavlović, Nataša | |
| dc.contributor.committeeMember | Gualdani, Maria P | |
| dc.contributor.committeeMember | Czubak, Magdalena | |
| dc.creator | Urban, Amie Bowles | |
| dc.creator.orcid | 0000-0003-1681-4132 | |
| dc.date.accessioned | 2022-07-19T23:18:34Z | |
| dc.date.available | 2022-07-19T23:18:34Z | |
| dc.date.created | 2021-08 | |
| dc.date.issued | 2021-08-06 | |
| dc.date.submitted | August 2021 | |
| dc.date.updated | 2022-07-19T23:18:35Z | |
| dc.description.abstract | In this dissertation, we study cubic and quintic nonlinear Schrödinger systems on 3-dimensional tori, with initial data in an adapted Hilbert space H [superscript s over lambda underscore], and all of our results hold on rational and irrational rectangular, flat tori. In the cubic and quintic case, we prove local well-posedness for both focusing and defocusing systems. We show that local solutions of the defocusing cubic system with initial data in H [superscript 1 over lambda underscore] can be extended for all time. Additionally, we prove that global well-posedness holds in the quintic system, focusing or defocusing, for initial data with sufficiently small H [superscript 1 over lambda underscore] norm. Finally, we use the energy-Casimir method to prove the existence and uniqueness, and nonlinear stability of a class of stationary states of the defocusing cubic and quintic nonlinear Schrödinger systems. | |
| dc.description.department | Mathematics | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | https://hdl.handle.net/2152/114977 | |
| dc.identifier.uri | http://dx.doi.org/10.26153/tsw/41880 | |
| dc.language.iso | en | |
| dc.subject | NLS systems | |
| dc.subject | Nonlinear Schrodinger systems | |
| dc.subject | Torus | |
| dc.subject | Stationary states | |
| dc.subject | Nonlinear stability | |
| dc.subject | Energy-Casimir method | |
| dc.title | Nonlinear Schrödinger systems on the three-dimensional torus | |
| dc.type | Thesis | |
| dc.type.material | text | |
| thesis.degree.department | Mathematics | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | The University of Texas at Austin | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy |