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 …

_?> H ) > G - Page 1 Communications in Commun. Math. Phys. 105, 35-47 (1986) ^^PhJoieS
© Springer-Verlag 1986 Existence of Localized Solutions for a Classical Nonlinear Dirac …

We show that there is room, in the Dirac equation, for a massless monopole. The basic idea
is that the Dirac equation admits a second electromagnetic minimal coupling associated to …

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) …

A $\mathcal {PT} $-symmetric nonlinear Schr\" odinger dimer is a two-site discrete nonlinear
Schr\" odinger equation with one site losing and the other one gaining energy at the same …

We explore a prototypical two-dimensional massive model of the nonlinear Dirac type and
examine its solitary wave and vortex solutions. In addition to identifying the stationary states …

We study solitons of the two-dimensional nonlinear Dirac equation with asymmetric cubic
nonlinearity. We show that with the nonlinearity parameters specifically tuned, a high degree …

We consider the nonlinear Dirac equation in 1+ 1 dimension with scalar-scalar self
interaction g 2 κ+ 1 (Ψ¯ Ψ) κ+ 1 and with mass m. Using the exact analytic form for rest frame …

Quantum walk (QW) provides a versatile tool to study fundamental physics and also to make
a variety of practical applications. We here start with the recent idea of nonlinear QW and …

We consider the nonlinear Dirac equations (NLDE's) in 1+ 1 dimension with scalar-scalar
self interaction g 2 k+ 1 (Ψ¯ Ψ) k+ 1, as well as a vector-vector self interaction g 2 k+ 1 (Ψ¯ γ …