Solitons in nonlinear lattices
arXiv:1010.2254 · doi:10.1103/RevModPhys.83.247
Abstract
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.
169 pages, 35 figures, a comprehensive survey of results on solitons in purely nonlinear and mixed lattices, to appear in Reviews of Modern Physics
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- Observation of edge solitons and transitions between them in a trimer circuit lattice
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- Discrete vortices on spatially nonuniform two-dimensional electric networks
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- Acoustic solitons in a periodic waveguide: theory and experiments
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- Vortex rings and vortex ring solitons in shaken Bose-Einstein condensate
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- Localized-Interaction-Induced Quantum Reflection and Filtering of Bosonic Matter in a One-Dimensional Lattice Guide
- Persistence of integrable wave dynamics in the Discrete Gross--Pitaevskii equation: the focusing case
- Existence of Coupled Optical Vortex Solitons Propagating in a Quadratic Nonlinear Medium
- Edge Solitons in a Nonlinear Mechanical Topological Insulator
- Dynamics of bright solitons and soliton arrays in the nonlinear Schrodinger equation with a combination of random and harmonic potentials
- Bloch oscillations in supersolids
- New Frontiers in Multidimensional Self-Trapping of Nonlinear Fields and Matter
- Three-component Fermi gas with SU(3) symmetry: BCS-BEC crossover in three and two dimensions
- Solitons in lattice field theories via tight-binding supersymmetry
- Extrapolation of perturbation-theory expansions by self-similar approximants
- Discrete Vortices in Systems of Coupled Nonlinear Oscillators: Numerical Results for an Electric Model
- Self-trapped spatially localized states in combined linear-nonlinear periodic potentials
- Tunable optical lattices for the creation of matter-wave lattice solitons
- Pulse-driven depinning of magnetic gap modes in ferromagnetic films
- Dark solitons in nonlinear Su-Schrieffer-Heeger lattices
- Towards the complete description of stationary states of a Bose-Einstein condensate in a one-dimensional quasiperiodic lattice: A coding approach
- Vortex ring beams in nonlinear -symmetric systems
- Stable vortex soliton arrays in disclination-fractal systems
- Discrete Vortex Filaments on Arrays of Coupled Oscillators in the Nonlinear Resonant Mode
- Dissipative Magnetic Polariton Soliton
- Low-energy effective quantum field theoretic description of excitations about soliton configurations
- Vortex solitons in star networks
- Quantum dynamics of a -kink in Josephson junctions parallel arrays with large kinetic inductances
- Gap solitons attached to a gapless layer
- Pearl supratransmission in a boundary-driven two-dimensional nonlinear Schrödinger equation with a hole
- Bright Discrete Solitons in Spatially Modulated DNLS Systems
- Solitonic dynamics and excitations of the nonlinear Schrodinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials
- Stable single light bullets and vortices and their active control in cold Rydberg gases
- Saturable nonlinear Schrödinger equation with space- and time-dependent variable coefficients
- Optimal optical Ferris wheel solitons in a nonlocal Rydberg medium
- Efficient mode conversion in guiding structures with longitudinal modulation of nonlinearity
- Editorial (a preface to a Special Issue of journal Applied Sciences on "Guided-Wave Optics")