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Solitons in nonlinear lattices

Yaroslav V. Kartashov, Boris A. Malomed, and Lluis Torner

Yaroslav V. Kartashov

  • ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain

Boris A. Malomed

  • Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

Lluis Torner

  • ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain

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Rev. Mod. Phys. 83, 247 – Published 14 April, 2011Erratum Rev. Mod. Phys. 83, 405 (2011)

DOI: https://doi.org/10.1103/RevModPhys.83.247

Abstract

This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are also surveyed, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation. The solitons are considered in one, two, and three dimensions. Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions can be drawn. In particular, a novel fundamental property of one-dimensional solitons, which does not occur in the absence of NLs, is a finite threshold value of the soliton norm, necessary for their existence. In multidimensional settings, the stability of solitons supported by the spatial modulation of the nonlinearity is a truly challenging problem, for theoretical and experimental studies alike. In both the one-dimensional and two-dimensional cases, the mechanism that creates solitons in NLs in principle is different from its counterpart in linear lattices, as the solitons are created directly, rather than bifurcating from Bloch modes of linear lattices.

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25 April, 2011

Erratum

Publisher’s Note: Solitons in nonlinear lattices [Rev. Mod. Phys. 83, 247 (2011)]

Yaroslav V. Kartashov, Boris A. Malomed, and Lluis Torner
Rev. Mod. Phys. 83, 405 (2011)

Article Text

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Rev. Mod. Phys. 83, 247– Published 14 April, 2011
  • Received 20 February 2010
  • Publisher error corrected 25 April 2011

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