Geodesic
Two-dimensional solitons in irregular lattice systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 345-359

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_2007_151_3_a2,
     author = {M. J. Ablowitz and B. Ilan and E. Schonbrun and R. Piestun},
     title = {Two-dimensional solitons in irregular lattice systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {345--359},
     publisher = {mathdoc},
     volume = {151},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a2/}
}
TY  - JOUR
AU  - M. J. Ablowitz
AU  - B. Ilan
AU  - E. Schonbrun
AU  - R. Piestun
TI  - Two-dimensional solitons in irregular lattice systems
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 345
EP  - 359
VL  - 151
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a2/
LA  - ru
ID  - TMF_2007_151_3_a2
ER  - 
%0 Journal Article
%A M. J. Ablowitz
%A B. Ilan
%A E. Schonbrun
%A R. Piestun
%T Two-dimensional solitons in irregular lattice systems
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 345-359
%V 151
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a2/
%G ru
%F TMF_2007_151_3_a2
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/