Band-gap boundaries and fundamental solitons in complex two-dimensional nonlinear lattices

Mark J. Ablowitz; Nalan Antar; Ilkay BakIrtaş; Boaz Ilan

doi:10.1103/PhysRevA.81.033834

Band-gap boundaries and fundamental solitons in complex two-dimensional nonlinear lattices

Mark J. Ablowitz, Nalan Antar, Ilkay BakIrtaş, Boaz Ilan

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

Nonlinear Schrödinger (NLS) equation with external potentials (lattices) possessing crystal and quasicrystal structures are studied. The fundamental solitons and band gaps are computed using a spectral fixed-point numerical scheme. Nonlinear and linear stability properties of the fundamental solitons are investigated by direct simulations and the linear stability properties of the fundamental solitons are confirmed by analysis the linearized eigenvalue problem.

Original language	English
Article number	033834
Journal	Physical Review A - Atomic, Molecular, and Optical Physics
Volume	81
Issue number	3
DOIs	https://doi.org/10.1103/PhysRevA.81.033834
Publication status	Published - 22 Mar 2010

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abstract = "Nonlinear Schr{\"o}dinger (NLS) equation with external potentials (lattices) possessing crystal and quasicrystal structures are studied. The fundamental solitons and band gaps are computed using a spectral fixed-point numerical scheme. Nonlinear and linear stability properties of the fundamental solitons are investigated by direct simulations and the linear stability properties of the fundamental solitons are confirmed by analysis the linearized eigenvalue problem.",

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AU - BakIrtaş, Ilkay

AU - Ilan, Boaz

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AB - Nonlinear Schrödinger (NLS) equation with external potentials (lattices) possessing crystal and quasicrystal structures are studied. The fundamental solitons and band gaps are computed using a spectral fixed-point numerical scheme. Nonlinear and linear stability properties of the fundamental solitons are investigated by direct simulations and the linear stability properties of the fundamental solitons are confirmed by analysis the linearized eigenvalue problem.

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Band-gap boundaries and fundamental solitons in complex two-dimensional nonlinear lattices

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