In recent years, there has been considerable interest in the study of wave propagation in
nonlinear photonic lattices. The interplay between nonlinearity and periodicity has led …

In a recent article (Fefferman and Weinstein, in J Am Math Soc 25: 1169–1220, 2012), the
authors proved that the non-relativistic Schrödinger operator with a generic honeycomb …

In this article, we study the Schrödinger operator for a large class of periodic potentials with
the symmetry of a hexagonal tiling of the plane. The potentials we consider are …

Consider electromagnetic waves in two-dimensional honeycomb structured media, whose
constitutive laws have the symmetries of a hexagonal tiling of the plane. The properties of …

A systematic approach for deriving tight-binding approximations in general longitudinally
driven lattices is presented. As prototypes, honeycomb and staggered square lattices are …

The nonlinear Schrödinger (NLS) equation is considered on a periodic graph subject to the
Kirchhoff boundary conditions. Bifurcations of standing localized waves for frequencies lying …

We discuss the model robustness of the infinite two–dimensional square grid with respect to
symmetry breakings due to the presence of defects, that is, lacks of finitely or infinitely many …

We consider a nonlinear Schrödinger (NLS) equation on a spatially extended periodic
quantum graph. With a multiple scaling expansion, an effective amplitude equation can be …

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 …