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 …

The nonlinear optical Galton board (NLOGB), a quantum walk like (but nonlinear) discrete
time quantum automaton, is shown to admit a complex evolution leading to long time …

We analyze the vortex solution space of the $(2+ 1) $-dimensional nonlinear Dirac equation
for bosons in a honeycomb optical lattice at length scales much larger than the lattice …

We present the theoretical and mathematical foundations of stability analysis for a Bose–
Einstein condensate (BEC) at Dirac points of a honeycomb optical lattice. The combination …

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 …

In the present work, we explore a nonlinear Dirac equation motivated as the continuum limit
of a binary waveguide array model. We approach the problem both from a near-continuum …

We explore the formation and collective modes of Bose-Einstein condensate of Dirac
magnons (Dirac BEC). While we focus on two-dimensional Dirac magnons, an employed …

We study the coupled atomic–molecular quantized ring vortices of 87 Rb Bose–Einstein
condensates trapped in a rotating 3D anisotropic cylindrical trap using both time …

The interplay between nonlinearity and the band structure of pristine honeycomb lattices is
systematically explored. For that purpose, a theory of collective excitations valid for the first …