Nonlinear Dirac equation solitary waves in external fields.

@article{Mertens2012NonlinearDE,
  title={Nonlinear Dirac equation solitary waves in external fields.},
  author={Franz G Mertens and Niurka R. Quintero and Fred Cooper and Avinash Khare and Avadh B Saxena},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2012},
  volume={86 4 Pt 2},
  pages={
          046602
        }
}
We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find… 
Solitary waves in the nonlinear Dirac equation in the presence of external driving forces
We consider the nonlinear Dirac (NLD) equation in (1 + 1) dimensions with scalar–scalar self interaction in the presence of external forces as well as damping of the form , where both f and Ψ are
Speed-of-light pulses in the massless nonlinear Dirac equation with a potential.
We consider the massless nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction g^{2}/2(Ψ[over ¯]Ψ)^{2} in the presence of three external electromagnetic real potentials
Solitary waves in the Nonlinear Dirac Equation
In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and
Nonlinear Dirac equation solitary waves under a spinor force with different components
We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction in the presence of external forces as well as damping of the form $\gamma^0 f(x,t) - i \mu \gamma^0
Solitary waves in a discrete nonlinear Dirac equation
In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross–Neveu model. The motivation for this discrete model proposal is
Soliton dynamics in the ABS nonlinear spinor model with external fields
We consider the novel nonlinear model in (1 + 1)-dimensions for Dirac spinors recently introduced by Alexeeva et al (Ann. Phys., NY 403 198) (ABS model), which admits an exact explicit solitary-wave
Transverse Instability of Line Solitary Waves in Massive Dirac Equations
TLDR
It is proved analytically and numerically that the line solitary waves are spectrally unstable with respect to periodic transverse perturbations of large periods in the generalized massive Gross–Neveu model.
Multi-hump solitary waves of nonlinear Dirac equation
This paper concentrates on a (1+1)-dimensional nonlinear Dirac (NLD) equation with a general self-interaction, being a linear combination of the scalar, pseudoscalar, vector and axial vector
Solitary wave solutions of the 2+1 and 3+1 dimensional nonlinear Dirac equation constrained to planar and space curves
We study the effect of curvature and torsion on the solitons of the nonlinear Dirac equation considered on planar and space curves. Since the spin connection is zero for the curves considered here,
N ov 2 01 4 Transverse instability of line solitons in massive Dirac equations
Working in the context of localized modes in periodic potentials, we consider two systems of the massive Dirac equations in two spatial dimensions. The first system, a generalized massive Thirring
...
1
2
3
...