Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures

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Mark J. Ablowitz,¹ Boaz Ilan,² Ethan Schonbrun,³ and Rafael Piestun³
¹Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA
²School of Natural Sciences, University of California, Merced, P.O. Box 2039, Merced, California 95344, USA
³Department of Electrical and Computer Engineering, University of Colorado, Boulder, Colorado 80309-0425, USA

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Received 12 April 2006; published 7 September 2006; publisher error corrected 8 September 2006

Localizednonlinear modes, or solitons, are obtained for the two-dimensional nonlinearSchrödinger equation with various external potentials that possess large variationsfrom periodicity, i.e., vacancy defects, edge dislocations, and quasicrystal structure.The solitons are obtained by employing a spectral fixed-point computationalscheme. Investigation of soliton evolution by direct numerical simulations showsthat irregular-lattice solitons can be stable, unstable, or undergo collapse.

URL:	http://link.aps.org/doi/10.1103/PhysRevE.74.035601
DOI:	10.1103/PhysRevE.74.035601
PACS:	05.45.Yv; 42.65.Tg; 63.20.Pw; 61.44.Br 05.45.Yv Solitons 42.65.Tg Optical solitons; nonlinear guided waves 63.20.Pw Localized modes in crystal lattices 61.44.Br Structure of quasicrystals YEAR: 2006
KEYWORDS:	optical solitons, localised modes, vibrational modes, crystal structure, vacancies (crystal), crystal defects, quasicrystals, edge dislocations, Schrodinger equation

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Erratum

Publisher's Note: Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures [Phys. Rev. E 74, 035601 (2006)]
Mark J. Ablowitz, Boaz Ilan, Ethan Schonbrun et al.
Phys. Rev. E 74, 039903 (E) (2006)