Symmetry, winding number and topological charge of vortex solitons in discrete-symmetry media

Details Symmetry, winding number and topological charge of vortex solitons in discrete-symmetry media Symmetry, winding number and topological charge of vortex solitons in discrete-symmetry media

2008-11-02

arxiv.org/abs/0811.0156v1

Nonlinear Sciences

Pattern Formation and Solitons

6 pages, 2 figures

Scientific paper

We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schr\"odinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.

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