Publication Date
2009
Journal or Book Title
PHYSICS LETTERS A
Abstract
We revisit the theme of non-nearest-neighbor interactions in nonlinear dynamical lattices, in the prototypical setting of the discrete nonlinear Schrödinger equation. Our approach offers a systematic way of analyzing the existence and stability of solutions of the system near the so-called anti-continuum limit of zero coupling. This affords us a number of analytical insights such as the fact that, for instance, next-nearest-neighbor interactions allow for solutions with nontrivial phase structure in infinite one-dimensional lattices; in the case of purely nearest-neighbor interactions, such phase structure is disallowed. On the other hand, such non-nearest-neighbor interactions can critically affect the stability of unstable structures, such as topological charge S=2 discrete vortices. These analytical predictions are corroborated by numerical bifurcation and stability computations.
Pages
3688-3693
Volume
373
Issue
40
Recommended Citation
Kevrekidis, PG, "Non-nearest-neighbor interactions in nonlinear dynamical lattices" (2009). PHYSICS LETTERS A. 40.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/40
Comments
This is the prepublished version harvested from ArXiv. The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-4X0F3RM-1&_user=1516330&_coverDate=09%2F28%2F2009&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=ecb0c81433862bd077499dad930ebddb&searchtype=a