Two-dimensional solitons in irregular lattice systems |
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Authors: | M J Ablowitz B Ilan E Schonbrun R Piestun |
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Institution: | (1) Department of Applied Mathematics, University of Colorado, Boulder, Colo. 80309-0526, USA;(2) School of Natural Sciences, University of California, Merced, P.O. Box 2039, Merced, Calif. 95344, USA;(3) Department of Electrical and Computer Engineering, University of Colorado, Boulder, Colo. 80309-0425, USA |
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Abstract: | We compute and study localized nonlinear modes (solitons) in the semi-infinite gap of the focusing two-dimensional nonlinear Schrödinger (NLS) equation with various irregular lattice-type potentials. The potentials are characterized by large variations from periodicity, such as vacancy defects, edge dislocations, and a quasicrystal structure. We use a spectral fixed-point computational scheme to obtain the solitons. The eigenvalue dependence of the soliton power indicates parameter regions of self-focusing instability; we compare these results with direct numerical simulations of the NLS equation. We show that in the general case, solitons on local lattice maximums collapse. Furthermore, we show that the Nth-order quasicrystal solitons approach Bessel solitons in the large-N limit. |
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Keywords: | soliton localized lattice mode nonlinear optics beam self-focusing quasicrystal |
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