dc.contributor.advisor | Comech, Andrew | |
dc.creator | Pekmez, Hatice Kubra | |
dc.date.accessioned | 2019-01-18T16:16:37Z | |
dc.date.available | 2019-01-18T16:16:37Z | |
dc.date.created | 2018-08 | |
dc.date.issued | 2018-08-06 | |
dc.date.submitted | August 2018 | |
dc.identifier.uri | https://hdl.handle.net/1969.1/174114 | |
dc.description.abstract | We study the nonlinear Dirac equation with Soler-type nonlinearity in one dimension (which is
called the Gross-Neveu model), with the nonlinearity localized at one and at two points. We study
the spectral stability of the solitary wave solutions in these models. As a consequence, we obtain
the result that the eigenvalues of the equation with the Soler-type nonlinearity move along the
imaginary axis.
We also construct solitary waves under perturbations of the model and look for relations between
components of solitary waves in light of the techniques which we use for analyzing the
Gross-Neveu model.
We apply the same analysis to the Dirac equation with the concentrated nonlinearity of the
same type as in the massive Thirring model. We find the same spectrum of linearization at solitary
waves as that in the nonlinear Dirac equation with Soler-type nonlinearity. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.subject | the nonlinear Dirac equation | en |
dc.subject | solitary waves | en |
dc.subject | linearization | en |
dc.subject | instability | en |
dc.subject | perturbation | en |
dc.title | Dirac Operator with Concentrated Nonlinearity and Bifurcation of Embedded Eigenvalues from the Bulk of the Essential Spectrum | en |
dc.type | Thesis | en |
thesis.degree.department | Mathematics | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Texas A & M University | en |
thesis.degree.name | Master of Science | en |
thesis.degree.level | Masters | en |
dc.contributor.committeeMember | Howard, Peter | |
dc.contributor.committeeMember | Abanov, Artem G | |
dc.type.material | text | en |
dc.date.updated | 2019-01-18T16:16:37Z | |
local.etdauthor.orcid | 0000-0001-5105-0583 | |