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TMF, 2007, Volume 151, Number 3, Pages 345–359 (Mi tmf6050)  

This article is cited in 1 scientific paper (total in 1 paper)

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

DOI: https://doi.org/10.4213/tmf6050

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

Bibliographic databases:


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

Citation in format AMSBIB
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\paper Two-dimensional solitons in irregular lattice systems
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\pages 345--359
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\pages 723--734
\crossref{https://doi.org/10.1007/s11232-007-0058-4}
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  • https://doi.org/10.4213/tmf6050
  • http://mi.mathnet.ru/eng/tmf/v151/i3/p345

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Cole J.T., Musslimani Z.H., “Band Gaps and Lattice Solitons For the Higher-Order Nonlinear Schrodinger Equation With a Periodic Potential”, Phys. Rev. A, 90:1 (2014), 013815  crossref  mathscinet  adsnasa  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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