Pekmez, Hatice Kubra (2018-08). Dirac Operator with Concentrated Nonlinearity and Bifurcation of Embedded Eigenvalues from the Bulk of the Essential Spectrum. Master's Thesis. Thesis uri icon

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.
  • 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.

publication date

  • August 2018