Three-dimensional solitary waves and vortices in a discrete nonlinear Schrödinger lattice.

Three-Dimensional Solitary Waves and Vortices in a Discrete Nonlinear Schrödinger Lattice

Discrete solitons and vortices in hexagonal and honeycomb lattices: existence, stability, and dynamics.

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrödinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytic...

ar X iv : n lin / 0 41 10 16 v 1 [ nl in . P S ] 6 N ov 2 00 4 Nonlinear Schrödinger lattices II : Persistence and stability of discrete vortices

We study discrete vortices in the anti-continuum limit of the discrete two-dimensional non-linear Schrödinger (NLS) equations. The discrete vortices in the anti-continuum limit represent a finite set of excited nodes on a closed discrete contour with a non-zero topological charge. Using the Lyapunov–Schmidt reductions, we find sufficient conditions for continuation and termination of the discre...

Stable higher-order vortices and quasivortices in the discrete nonlinear Schrödinger equation.

Vortex solitons with the topological charge S=3 , and "quasivortex" (multipole) solitons, which exist instead of the vortices with S=2 and 4, are constructed on a square lattice in the discrete nonlinear Schrödinger equation (true vortices with S=2 were known before, but they are unstable). For each type of solitary wave, its stability interval is found, in terms of the intersite coupling const...

Modulation analysis of large-scale discrete vortices.

The behavior of large-scale vortices governed by the discrete nonlinear Schrödinger equation is studied. Using a discrete version of modulation theory, it is shown how vortices are trapped and stabilized by the self-consistent Peierls-Nabarro potential that they generate in the lattice. Large-scale circular and polygonal vortices are studied away from the anticontinuum limit, which is the limit...