Discrete solitons and vortices in anisotropic hexagonal and honeycomb lattices
Abstract
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:
-
- Western New England Univ., Springfield, MA (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1258008
- Report Number(s):
- LA-UR-15-24940
Journal ID: ISSN 2040-8978
- Grant/Contract Number:
- AC52-06NA25396
- Resource 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
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Hoq, Q. E., Kevrekidis, P. G., and Bishop, A. R. Discrete solitons and vortices in anisotropic hexagonal and honeycomb lattices. United States: N. p., 2016.
Web. doi:10.1088/2040-8978/18/2/024008.
Hoq, Q. E., Kevrekidis, P. G., & Bishop, A. R. Discrete solitons and vortices in anisotropic hexagonal and honeycomb lattices. United States. https://doi.org/10.1088/2040-8978/18/2/024008
Hoq, Q. E., Kevrekidis, P. G., and Bishop, A. R. Thu .
"Discrete solitons and vortices in anisotropic hexagonal and honeycomb lattices". United States. https://doi.org/10.1088/2040-8978/18/2/024008. https://www.osti.gov/servlets/purl/1258008.
@article{osti_1258008,
title = {Discrete solitons and vortices in anisotropic hexagonal and honeycomb lattices},
author = {Hoq, Q. E. and Kevrekidis, P. G. and Bishop, A. R.},
abstractNote = {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.},
doi = {10.1088/2040-8978/18/2/024008},
journal = {Journal of Optics},
number = 2,
volume = 18,
place = {United States},
year = {Thu Jan 14 00:00:00 EST 2016},
month = {Thu Jan 14 00:00:00 EST 2016}
}
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