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 …

We prove that the two-dimensional Schrödinger operator with a potential having the
symmetry of a honeycomb structure has dispersion surfaces with conical singularities (Dirac …

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 work, we have studied the magnetic properties of decorated triangular lattice using a
Monte Carlo simulation. The magnetic phase diagrams have been determined for a mixed …

We present gap solitons (GSs) that can be created in free nearly two-dimensional (2D)
space in dipolar spinor Bose-Einstein condensates with the spin-orbit coupling (SOC) …

This work presents a rigorous theory for topological photonic materials in one dimension.
The main focus is on the existence of interface modes that are induced by topological …

We present several numerical methods and establish their error estimates for the
discretization of the nonlinear Dirac equation (NLDE) in the nonrelativistic limit regime …

We suggest a real physical system—the honeycomb lattice—as a possible realization of the
fractional Schrödinger equation (FSE) system, through utilization of the Dirac‐Weyl equation …

We elaborate a mechanism for the formation of stable solitons of the semivortex type (with
vorticities 0 and 1 in their two components), populating a finite band gap in the spectrum of …

We analyze rigorously error estimates and compare numerically spatial/temporal resolution
of various numerical methods for the discretization of the Dirac equation in the nonrelativistic …