Modulation analysis of large-scale discrete vortices

Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Sep;78(3 Pt 2):036604. doi: 10.1103/PhysRevE.78.036604. Epub 2008 Sep 17.

Abstract

The behavior of large-scale vortices governed by the discrete nonlinear Schrödinger equation is studied. Using a discrete version of modulation theory, it is shown how vortices are trapped and stabilized by the self-consistent Peierls-Nabarro potential that they generate in the lattice. Large-scale circular and polygonal vortices are studied away from the anticontinuum limit, which is the limit considered in previous studies. In addition numerical studies are performed on large-scale, straight structures, and it is found that they are stabilized by a nonconstant mean level produced by standing waves generated at the ends of the structure. Finally, numerical evidence is produced for long-lived, localized, quasiperiodic structures.