Publication Date
2006
Journal or Book Title
Physics Review E
Abstract
While fundamental-mode discrete solitons have been demonstrated with both self-focusing and defocusing nonlinearity, high-order-mode localized states in waveguide lattices have been studied thus far only for the self-focusing case. In this paper, the existence and stability regimes of dipole, quadrupole, and vortex soliton structures in two-dimensional lattices induced with a defocusing nonlinearity are examined by the theoretical and numerical analysis of a generic envelope nonlinear lattice model. In particular, we find that the stability of such high-order-mode solitons is quite different from that with self-focusing nonlinearity. As a simple example, a dipole (“twisted”) mode soliton with adjacent excited sites which may be stable in the focusing case becomes unstable in the defocusing regime. Our results may be relevant to other two-dimensional defocusing periodic nonlinear systems such as Bose-Einstein condensates with a positive scattering length trapped in optical lattices.
Volume
74
Issue
6
Recommended Citation
Kevrekidis, PG, "High-order-mode soliton structures in two-dimensional lattices with defocusing nonlinearity" (2006). Physics Review E. 1105.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1105
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://pre.aps.org/abstract/PRE/v74/i6/e066606