Nonlinear Schrödinger lattices II: Persistence and Stability of Discrete Vortices

Pelinovsky, D. E.; Kevrekidis, P. G.; Frantzeskakis, D. J.

Nonlinear Schrödinger lattices II: Persistence and Stability of Discrete Vortices

Authors

Pelinovsky, D. E.

Kevrekidis, P. G.

Frantzeskakis, D. J.

Description

We study discrete vortices in the anti-continuum limit of the discrete two-dimensional nonlinear Schr{ö}dinger (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 discrete vortices for a small coupling constant in the discrete NLS lattice. An example of a closed discrete contour is considered that includes the vortex cell (also known as the off-site vortex). We classify the symmetric and asymmetric discrete vortices that bifurcate from the anti-continuum limit. We predict analytically and confirm numerically the number of unstable eigenvalues associated with various families of such discrete vortices.
34 pages, 6 figures