Discrete breathers and vortices in hexagonal dust crystals

We consider the existence and stability of multipole, vortex and soliton type localized modes in hexagonal and honeycomb lattices, with an aim to model strongly nonlinear transverse oscillations of charged dust grains in dusty plasma lattices (DPLs). The theory is essentially formulated in terms of the coupling (discreteness) parameter epsiv = omega_T ²/omega₀ ² (here omega_T is the eigenfrequency of the tranverse DPL mode, and omega₀ is related to electrostatic inter-grain interactions), thus allowing for a direct interpretation in terms of experimentally measurable plasma quantities. Two approaches, relying on the discrete nonlinear Schrodinger and the Klein-Gordon paradigms, are employed and found to agree to a satisfactory extent. The former approach has been associated to beam propagation in optical waveguide arrays. In contours involving three sites, the vortex configuration of topological charge S=1 is the most stable one. For 6-site configurations, we obtain the surprising feature that vortices of lower topological charge (S=1) may be unstable, while those of higher topological charge (e.g., S=2) may be stable. The analysis is complemented by numerical simulations and bifurcation studies. Extending previous work on breather excitations in 1D crystals, the anticontinuum-limit method is employed, to investigate single- and multi-site excitations. Instability occurs beyond a threshold value of epsiv, which is lower for multi-breathers than for single-site ones. These results complement earlier ones regarding quasi-continuum 2D envelope dust-lattice modes.