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This article is cited in 2 scientific papers (total in 2 papers)
Two-dimensional solitons in irregular lattice systems
M. J. Ablowitza, B. Ilanb, E. Schonbruna, R. Piestuna a University of Colorado
b School of Natural Sciences, University of California
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 $N$th-order quasicrystal solitons approach Bessel solitons in the large-$N$
limit.
Keywords:
soliton, localized lattice mode, nonlinear optics, beam self-focusing, quasicrystal.
Citation:
M. J. Ablowitz, B. Ilan, E. Schonbrun, R. Piestun, “Two-dimensional solitons in irregular lattice systems”, TMF, 151:3 (2007), 345–359; Theoret. and Math. Phys., 151:3 (2007), 723–734
Linking options:
https://www.mathnet.ru/eng/tmf6050https://doi.org/10.4213/tmf6050 https://www.mathnet.ru/eng/tmf/v151/i3/p345
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Abstract page: | 431 | Full-text PDF : | 197 | References: | 42 | First page: | 8 |
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