Related papers: Speed-of-light pulses in the massless nonlinear Di…
We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{\kappa+1} ({\bPsi} \Psi)^{\kappa+1}$ in the presence of various external electromagnetic fields. Starting from the exact…
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 $ f(x,t) - i \mu \gamma^0 \Psi$, where both $f$ and $\Psi$ are…
In this paper, we investigate the nonrelativistic limit and qualitative properties of bound-state solutions for the nonlinear Dirac equation (NLDE) defined on noncompact quantum graphs: \[ -i c \frac{d}{d x} \sigma_1 \psi+m c^2 \sigma_3…
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 $\gamma^0 f(x,t) - i \mu \gamma^0 \Psi$, where both $f, \{f_j = r_i e^{i…
In this paper, we study the existence and multiplicity of solutions to the following class of nonlinear Dirac equations (NLDE) on noncompact quantum graphs: \[ -i\,\varepsilon c\,\sigma_1\,\partial_x u + m c^2 \sigma_3 u + V(x)\,u =…
Second order Newton equations of motion for a radiating particle are presented. It is argued that the trajectories obeying them also satisfy the Abraham-Lorentz-Dirac (ALD) equations for general 3D motions in the non-relativistic and…
We derive an exact solitary wave solution for the $\PTb$-symmetric nonlinear Dirac equation with a scalar-scalar interaction. We consider a power-law nonlinearity of the form $|\bar{\Psi}\,\Psi|^{k}\,\Psi$ for positive values of $k$. The…
We revisit Newton's equation of motion in one dimension when the moving particle has a variable mass m(x,t) depending both on position (x) and time (t). Geometrically the mass function is identified with one of the metric function in a…
The condition for potential description of the wake waves,generated by flat or cylindrical driving electron bunch in cold plasma is derived. The two-dimensional nonlinear equation for potential valid for small values of that is obtained and…
We consider the coupled nonlinear Dirac equations (NLDE's) in 1+1 dimensions with scalar-scalar self interactions $\frac{ g_1^2}{2} ( {\bpsi} \psi)^2 + \frac{ g_2^2}{2} ( {\bphi} \phi)^2 + g_3^2 ({\bpsi} \psi) ( {\bphi} \phi)$ as well as…
We solve the Dirac equation in one space dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The spectrum…
We study the self-interaction effects for the Dirac particle moving in an external field created by static charges in (1+1)-dimensions. Assuming that the total electric charge of the system vanishes, we show that the asymptotically linearly…
In this paper, we investigate the nonrelativistic limit of normalized solutions to a nonlinear Dirac equation as given below: \begin{equation*} \begin{cases} &-i c\sum\limits_{k=1}^3\alpha_k\partial_k u +mc^2 \beta {u}- \Gamma * (K…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
The Dirac equation is solved for a pseudoscalar Coulomb potential in a two-dimensional world. An infinite sequence of bounded solutions are obtained. These results are in sharp contrast with those ones obtained in 3+1 dimensions where no…
In this work a new mechanics will be studied which is based on the hypothesis that the change of linear momentum of a particle happens as a discrete pulses. By using this hypothesis and by considering Newton's relation between energy and…
In the paper \cite{carati95} it was shown that, for motions on a line under the action of a potential barrier, the third-order Abraham-Lorentz-Dirac equation presents the phenomenon of nonuniqueness of nonrunaway solutions. Namely, at least…
A broad class of forces, P, is identified, for which the Abraham-Lorentz-Dirac (ALD) and Newton-like equations have solutions in common. Moreover, these solutions do not present pre-acceleration or escape into infinity (runaway behavior).…
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional…
A massless Dirac particle is considered, moving along the x-axis while Pauli-coupled by its anomalous magnetic moment to a piecewise constant magnetic field along the same axis, with stochastically varying sign. The motion is approximated…