# Solitons in nonlinear lattices

@article{Kartashov2011SolitonsIN, title={Solitons in nonlinear lattices}, author={Yaroslav V. Kartashov and Boris A. Malomed and Lluis Torner}, journal={Reviews of Modern Physics}, year={2011}, volume={83}, pages={247-305} }

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…

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## References

SHOWING 1-10 OF 332 REFERENCES

Multidimensional solitons in periodic potentials

- Physics
- 2003

The existence of stable solitons in two- and three-dimensional (2D and 3D) media governed by the self-focusing cubic nonlinear Schrodinger equation with a periodic potential is demonstrated by means…

Matter-wave solitons in nonlinear optical lattices.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

A dynamical model of a Bose-Einstein condensate based on the one-dimensional Gross-Pitaevskii equation with a nonlinear optical lattice with a cubic term whose coefficient is periodically modulated in the coordinate is introduced.

Spatiotemporal optical solitons

- Physics
- 2005

In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are…

Solitons in one-dimensional photonic crystals

- Physics
- 2008

We report on results of a systematic analysis of spatial solitons in the model of one-dimensional photonic crystals, built as a periodic lattice of waveguiding channels, of width D, separated by…

Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices

- PhysicsNature
- 2003

This work uses optical induction, the interference of two or more plane waves in a photosensitive material, to create a 2D photonic lattice in which the solitons form, paving the way for the realization of a variety of nonlinear localization phenomena inPhotonic lattices and crystals.

Stability of matter-wave solitons in optical lattices

- Physics
- 2010

Abstract.
We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical…

Power dependent soliton location and stability in complex photonic structures.

- PhysicsOptics express
- 2008

This work shows that for more complex photonic structures where either one of the refractive indices (linear or nonlinear) is modulated by more than one wavenumbers, or both of them are modulated, soliton position and stability depends strongly on its characteristics.

Solitons in a linearly coupled system with separated dispersion and nonlinearity.

- PhysicsChaos
- 2005

We introduce a model of dual-core waveguide with the cubic nonlinearity and group-velocity dispersion (GVD) confined to different cores, with the linear coupling between them. The model can be…

Two-dimensional solitons in media with stripe-shaped nonlinearity modulation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

This work introduces a model of media with the cubic attractive nonlinearity concentrated along a single or double stripe in the two-dimensional (2D) plane and makes use of the variational approximation (VA) and numerical methods to investigate conditions for the existence and stability of solitons in the present setting.