Persistence and stability of discrete vortices in nonlinear Schrödinger lattices

We study discrete vortices in the two-dimensional nonlinear Schrödinger lattice with small coupling between lattice nodes. The discrete vortices in the anti-continuum limit of zero coupling represent a finite set of excited nodes on a closed discrete contour with a non-zero charge. Using the Lyapunov–Schmidt reductions, we analyze continuation and termination of the discrete vortices for small coupling between lattice nodes. An example of a …