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dc.contributor.advisorComech, Andrew
dc.creatorPekmez, Hatice Kubra
dc.date.accessioned2019-01-18T16:16:37Z
dc.date.available2019-01-18T16:16:37Z
dc.date.created2018-08
dc.date.issued2018-08-06
dc.date.submittedAugust 2018
dc.identifier.urihttp://hdl.handle.net/1969.1/174114
dc.description.abstractWe 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.mimetypeapplication/pdf
dc.language.isoen
dc.subjectthe nonlinear Dirac equationen
dc.subjectsolitary wavesen
dc.subjectlinearizationen
dc.subjectinstabilityen
dc.subjectperturbationen
dc.titleDirac Operator with Concentrated Nonlinearity and Bifurcation of Embedded Eigenvalues from the Bulk of the Essential Spectrumen
dc.typeThesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorTexas A & M Universityen
thesis.degree.nameMaster of Scienceen
thesis.degree.levelMastersen
dc.contributor.committeeMemberHoward, Peter
dc.contributor.committeeMemberAbanov, Artem G
dc.type.materialtexten
dc.date.updated2019-01-18T16:16:37Z
local.etdauthor.orcid0000-0001-5105-0583


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