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

University of Colorado Boulder
University of California Merced

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

20 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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title = "Band-gap boundaries and fundamental solitons in complex two-dimensional nonlinear lattices",

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.",

author = "Ablowitz, \{Mark J.\} and Nalan Antar and Ilkay BakIrta{\c s} and Boaz Ilan",

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AU - Ablowitz, Mark J.

AU - Antar, Nalan

AU - BakIrtaş, Ilkay

AU - Ilan, Boaz

PY - 2010/3/22

Y1 - 2010/3/22

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/77949700089

U2 - 10.1103/PhysRevA.81.033834

DO - 10.1103/PhysRevA.81.033834

M3 - Article

AN - SCOPUS:77949700089

SN - 1050-2947

VL - 81

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 3

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

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