This article is cited in 2 papers

Two-dimensional solitons in irregular lattice systems

M. J. Ablowitz^a, B. Ilan^b, E. Schonbrun^a, R. Piestun<sup>a

a</sup> 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.

DOI: 10.4213/tmf6050

 English version: Theoretical and Mathematical Physics, 2007, 151:3, 723–734

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