Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

Ahmed Murad

Second Advisor

Nagi T. Wakim

Third Advisor

Dr. Usama Al Khawaja


The nonlinear Dirac equation is a relativistic classical field theory that describes the behavior of a system of self-interacting spinor fields. According to this theory, the interactions among spinor fields are represented by additional Kerr-nonlinearity added to the Dirac equation, which justifies and models the noticed solitonic behavior of the systems. There are various models of the nonlinear Dirac equation which differ from each other in the factors taken into account in the modelling, especially the mode of the coupling among the spinor fields as well as the nature of the system represented by the model. In this present thesis, a special form of the nonlinear Dirac equation (NLDE) is considered, namely, the massive Thirring model (MTM) in (1+1)-dimensions, which models the vector-vector coupling mode of interactions among spinor fields in condensed matter. Here, exact localized stationary solutions are obtained using analytical methods. The physical properties of MTM and the corresponding conserved physical quantities are discussed through developing the continuity equation of the current density together with evaluating explicitly the elements of the energy-momentum tensor, which are then used to calculate some properties like charge and energy of the fields. Also, the same analytical methods are used to find stationary exact solutions of another model of NLDE, the Gross-Neveu model, which is of interest in high-energy physics

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