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Discrete solitons and vortices in hexagonal and honeycomb lattices : existence, stability, and dynamics
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Law, K. J. H., Kevrekidis, P., Koukouloyannis, V., Kourakis, I., Frantzeskakis, D. and Bishop, A. (2008) Discrete solitons and vortices in hexagonal and honeycomb lattices : existence, stability, and dynamics. Physical Review E, Vol.78 (No.6). Article no. 066610 . doi:10.1103/PhysRevE.78.066610 ISSN 1539-3755.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.78.066610
Abstract
We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrödinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the “hexapole” of alternating phases (0-π), as well as the vortex of topological charge S=2 have intervals of stability; among three-site states, only the vortex of topological charge S=1 may be stable in the case of focusing nonlinearity. These conclusions are confirmed both for hexagonal and for honeycomb lattices by means of detailed numerical bifurcation analysis of the stationary states from the anticontinuum limit, and by direct simulations to monitor the dynamical instabilities, when the latter arise. The dynamics reveal a wealth of nonlinear behavior resulting not only in single-site solitary wave forms, but also in robust multisite breathing structures.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Physical Review E | ||||
Publisher: | American Physical Society | ||||
ISSN: | 1539-3755 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.78 | ||||
Number: | No.6 | ||||
Page Range: | Article no. 066610 | ||||
DOI: | 10.1103/PhysRevE.78.066610 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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