Solitons in nonlinear lattices

This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely 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 surveyed too, 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 (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). 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 1D 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 the theoretical and experimental studies alike. In both the 1D and 2D cases, the mechanism which creates solitons in NLs is principally different from its counterpart in linear lattices, as the solitons are created directly, rather than bifurcating from Bloch modes of linear lattices.Comment: 169 pages, 35 figures, a comprehensive survey of results on solitons in purely nonlinear and mixed lattices, to appear in Reviews of Modern Physic

Light Beams in Liquid Crystals

This reprint collects recent articles published on "Light Beams in Liquid Crystals", both research and review contributions, with specific emphasis on liquid crystals in the nematic mesophase. The editors, Prof. Gaetano Assanto (NooEL, University of Rome "Roma Tre") and Prof. Noel F. Smyth (School of Mathematics, University of Edinburgh), are among the most active experts worldwide in nonlinear optics of nematic liquid crystals, particularly reorientational optical solitons ("nematicons") and other all-optical effects

Observation of incoherently coupled dark-bright vector solitons in single-mode fibers

We report experimental observation of incoherently coupled dark-bright vector solitons in single-mode fibers. Properties of the vector solitons agree well with those predicted by the respective systems of incoherently coupled nonlinear Schroedinger equations. To the best of our knowledge, this is the first experimental observation of temporal incoherently coupled dark-bright solitons in single-mode fibers.Comment: to be published in Optics Expres

On the Korteweg-de Vries approximation for uneven bottoms

In this paper we focus on the water waves problem for uneven bottoms on a two-dimensionnal domain. Starting from the symmetric Boussinesq systems derived in [Chazel, Influence of topography on long water waves, 2007], we recover the uncoupled Korteweg-de Vries (KdV) approximation justified by Schneider and Wayne for flat bottoms, and by Iguchi in the context of bottoms tending to zero at infinity at a substantial rate. The goal of this paper is to investigate the validity of this approximation for more general bathymetries. We exhibit two kinds of topography for which this approximation diverges from the Boussinesq solutions. A topographically modified KdV approximation is then proposed to deal with such bathymetries. Finally, all the models involved are numerically computed and compared