Stability of optical gap solitons is analyzed within a coupled-mode theory. Lower intensity
solitons are shown to always possess a vibration mode responsible for their long-lived …

This paper presents a review of the current state-of-the-art of numerical methods for
nonlinear Dirac (NLD) equation. Several methods are extendedly proposed for the (1+ 1) …

We prove that for a Dirac operator, with no resonance at thresholds nor eigenvalue at
thresholds, the propagator satisfies propagation and dispersive estimates. When this linear …

We study the point spectrum of the nonlinear Dirac equation in any spatial dimension,
linearized at one of the solitary wave solutions. We prove that, in any dimension, the …

We consider the nonlinear Dirac equation, also known as the Soler model: i∂ t ψ=− i α⋅∇
ψ+ m β ψ−(ψ⁎ β ψ) k β ψ, m> 0, ψ (x, t)∈ CN, x∈ R n, k∈ N. We study the point spectrum of …

This Letter presents a numerical study of the interaction dynamics for the solitary waves of a
nonlinear Dirac field with scalar self-interaction by using a fourth order accurate Runge …

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 …

This paper presents an efficient adaptive mesh redistribution method to solve a non-linear
Dirac (NLD) equation. Our algorithm is formed by three parts: the NLD evolution, the iterative …

We study stability of optical gap solitons, close relatives of spinor solitons of nonlinear
classical field theory. The analysis of the associated linearized eigenvalue problem …

We study the linear stability of localized modes in self-interacting spinor fields, analysing the
spectrum of the operator corresponding to linearization at solitary waves. Following the …