Topological photonics is a rapidly emerging field of research in which geometrical and
topological ideas are exploited to design and control the behavior of light. Drawing …

Optical lattices have developed into a widely used and highly recognized tool to study many-
body quantum physics with special relevance for solid state type systems. One of the most …

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 study analytically and numerically an optical analogue of Dirac solitons in binary
waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of …

Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from
high-energy physics to condensed-matter physics. In this article, we review the recent …

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 dynamics of Dirac solitons in prototypical networks modeling them by the
nonlinear Dirac equation on metric graphs. Stationary soliton solutions of the nonlinear …

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 …

The honeycomb supersolid state is predicted to form in a dipolar Bose-Einstein condensate
with a planar confining potential. Our results for its excitation spectrum reveal the gapless …

Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb optical lattice are
computed. We find that the topological structure of the Bloch bands at the Dirac point is …