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In this article we discuss the modelling of elastic and electromagnetic wave propagation through one- and two-dimensional structured piezoelectric solids. Dispersion and the effect of piezoelectricity on the group velocity and positions of…
We describe a nonlinear kagome lattice with nonlinear dynamics described by Klein-Gordon interactions with a scalar unknown at each node, such as might occur in a nonlinear electrical lattice. We show that the dispersion relation has three…
We describe wave propagation and soliton localization in photonic lattices which are induced in a nonlinear medium by an optical interference pattern, taking into account the inherent lattice deformations at the soliton location. We obtain…
We analyze theoretically and generate experimentally two-dimensional nonlinear periodic lattices in a photorefractive medium. We demonstrate that the light-induced periodically modulated nonlinear refractive index is highly anisotropic and…
An analytical theory is proposed for the kinetic electrostatic electron nonlinear (KEEN) waves originally found in simulations by Afeyan et al [arXiv:1210.8105]. We suggest that KEEN waves represent saturated states of the negative mass…
We study stability and dynamics of the single cylindrically symmetric solitary structures and dipolar solitonic molecules in spatially nonlocal media. The main properties of the solitons, vortex solitons, and dipolar solitons are…
We predict theoretically that stable subwavelength plasmonic lattice solitons (PLSs) are formed in arrays of metallic nanowires embedded in a nonlinear medium. The tight confinement of the guiding modes of the metallic nanowires, combined…
This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…
Solitons are non-dispersive wave solutions that arise in a diverse range of nonlinear systems, stablised by a focussing or defocussing nonlinearity. First observed in shallow water, solitons have subsequently been studied in many other…
A new approach to the nonlinear reponse of a multiplayer structure consisting of alternating dielectric materials with intensity-dependent dielectric constants is considered in both analytical and numerical viewpoints. The nonlinear…
Resonant mode interactions in weakly nonlinear multi-dimensional lattices and related effects are described. We concentrate on formal description of the phenomenon and consider as examples mode interactions and evolution equations for…
This paper is devoted to the unidimensional analysis of a 2-ports silicon resonator vibrating in thickness--extensional mode. Both excitation and detection ports are capacitive transducers used to control the system of longitudinal elastic…
Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by…
Dielectric metasurfaces are structured thin films with thickness smaller than the wavelength that aim at replacing and enhancing conventional bulk optical components by structuring local resonances across an aperture. At visible and…
This study presents innovative nested-isotropic lattices for additive manufacturing, drawing inspiration from bio-architectures found in cortical bone osteons, golden spirals, and fractals. These lattices provide tunable anisotropy by…
We predict that stable mobile spatio-temporal solitons can exist in arrays of periodically curved optical waveguides. We find two-dimensional light bullets in one-dimensional arrays with harmonic waveguide bending and three-dimensional…
In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model…
We predict the existence of a novel class of multidimensional light localizations in out-of-equilibrium ferroelectric crystals. In two dimensions, the non-diffracting beams form at arbitrary low power level and propagate even when their…
Materials science and the study of the electronic properties of solids are a major field of interest in both physics and engineering. The starting point for all such calculations is single-electron, or non-interacting, band structure…
We show that the timed Dicke states of a collection of three-level atoms can form a tight-binding lattice in momentum space. This lattice, coined the superradiance lattice (SL), can be constructed based on electromagnetically induced…