Related papers: Nonlinear Dirac equation solitary waves in externa…
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…
We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{k+1} ({\bar \Psi} \Psi)^{k+1}$, as well as a vector-vector self interaction $\frac{g^2}{k+1} ({\bar \Psi} \gamma_\mu \Psi…
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…
We consider the nonlinear Schr{\"o}dinger equation (NLSE) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{\kappa+1} (\psi^\star \psi)^{\kappa+1}$ in the presence of the external forcing terms of the form $r e^{-i(kx +…
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 discuss its localized waveforms in one, two,…
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 obtain exact solutions of the nonlinear Dirac equation in 1+1 dimension of the form $\Psi(x,t) = \Phi(x) e^{-i \omega t}$ where the nonlinear interactions are a combination of vector-vector (V-V) and scalar-scalar (S-S) interactions with…
We consider the nonlinear Dirac equation in one dimension, also known as the Soler model in (1+1) dimensions, or the massive Gross-Neveu model: $i\partial_t\psi=-i\alpha\partial_x\psi+m\beta\psi-f(\psi^\ast\beta\psi)\beta\psi$,…
We consider the nonlinear Dirac equation in 1+1 dimension with scalar-scalar self interaction $ \frac{g^2}{\kappa+1} ({\bar \Psi} \Psi)^{\kappa+1}$ and with mass $m$. Using the exact analytic form for rest frame solitary waves of the form…
We discuss the response of both moving and trapped solitary wave solutions of a nonlinear two-component nonlinear Schr\"odinger system in 1+1 dimensions to an anti-$\mathcal{PT}$ external periodic complex potential. The dynamical behavior…
We discuss the behavior of solitary wave solutions of the nonlinear Schr{\"o}dinger equation (NLSE) as they interact with complex potentials, using a four parameter variational approximation based on a dissipation functional formulation of…
We study the behavior of solitary-wave solutions of some generalized nonlinear Schr\"odinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing…
We study the spectral stability of solitary wave solutions to the nonlinear Dirac equation in one dimension. We focus on the Dirac equation with cubic nonlinearity, known as the Soler model in (1+1) dimensions and also as the massive…
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 both computational (near the continuum…
In this paper we study the behavior of solutions of a nonlinear Schroedinger equation in presence of an external potential, which is allowed to be singular at one point. We show that the solution behaves like a solitary wave for long time…
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 self-interactions to the power of the integer…
For the nonlinear Dirac equation in (1+1)D with scalar self-interaction (Gross--Neveu model), with quintic and higher order nonlinearities (and within certain range of the parameters), we prove that solitary wave solutions are…
We consider the nonlinear Dirac equation, also known as the Soler model: $i\p\sb t\psi=-i\alpha \cdot \nabla \psi+m \beta \psi-f(\psi\sp\ast \beta \psi) \beta \psi$, $\psi(x,t)\in\mathbb{C}^{N}$, $x\in\mathbb{R}^n$, $n\le 3$, $f\in C\sp…
We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in {\it time-dependent} external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a…
We study collective phenomena of self-propagating particles using the nonlinear Kramers equation. A solitary wave state appears from an instability of the spatially uniform ordered state with nonzero average velocity. Two solitary waves…