Geodesic
Two-dimensional solitons in irregular lattice systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 345-359 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $N$th-order quasicrystal solitons approach Bessel solitons in the large-$N$ limit.
Mots-clés : soliton
Keywords: localized lattice mode, nonlinear optics, beam self-focusing, quasicrystal. 
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M. J. Ablowitz; B. Ilan; E. Schonbrun; R. Piestun. Two-dimensional solitons in irregular lattice systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 345-359. http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a2/

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