Publication Date
2005
Journal or Book Title
Physica D: Nonlinear Phenomena
Abstract
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 square discrete contour is considered that includes the vortex cell (also known as the off-site vortex). We classify families of 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 each family of such discrete vortices.
Pages
20-53
Volume
212
Issue
1-2
Recommended Citation
Pelinovsky, D E. and Kevrekidis, PG, "Persistence and stability of discrete vortices in nonlinear Schrödinger lattices" (2005). Physica D: Nonlinear Phenomena. 1088.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1088
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVK-4HG6NWF-4&_user=1516330&_coverDate=12%2F01%2F2005&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1581604347&_rerunOrigin=google&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=29d04e42b3db37c28e96d8d3d2e3e573&searchtype=a