Modulation analysis of large-scale discrete vortices.
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.
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA. cisneros@math.unm.edu
Luis A
LA
Cisneros
Antonmaria A
AA
Minzoni
Panayotis
P
Panayotaros
Noel F
NF
Smyth