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Title: Discrete solitons and vortices in anisotropic hexagonal and honeycomb lattices

We consider the self-focusing discrete nonlinear Schrödinger equation on hexagonal and honeycomb lattice geometries. Our emphasis is on the study of the effects of anisotropy, motivated by the tunability afforded in recent optical and atomic physics experiments. We find that multi-soliton and discrete vortex states undergo destabilizing bifurcations as the relevant anisotropy control parameter is varied. Furthermore, we quantify these bifurcations by means of explicit analytical calculations of the solutions, as well as of their spectral linearization eigenvalues. Finally, we corroborate the relevant stability picture through direct numerical computations. In the latter, we observe the prototypical manifestation of these instabilities to be the spontaneous rearrangement of the solution, for larger values of the coupling, into localized waveforms typically centered over fewer sites than the original unstable structure. In weak coupling, the instability appears to result in a robust breathing of the relevant waveforms.
Authors:
 [1] ;  [2] ;  [3]
  1. Western New England Univ., Springfield, MA (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
OSTI Identifier:
1258008
Report Number(s):
LA-UR--15-24940
Journal ID: ISSN 2040-8978
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Journal of Optics
Additional Journal Information:
Journal Volume: 18; Journal Issue: 2; Journal ID: ISSN 2040-8978
Publisher:
IOP Publishing
Research Org:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING