Related papers: Two-dimensional subwavelength plasmonic lattice so…
It is demonstrated the existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with linear OL in the $x-$direction and nonlinear OL (NOL) in the $y-$direction, where the NOL can be generated by a periodic…
A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered.…
We predict the existence and address the stability of two-dimensional surface solitons featuring topologically complex shapes, including dipoles, vortices, and bound states of vortex solitons, at the interface of nonlocal thermal media.…
We show a novel kind of nonlinear waves in two-dimensional photonic lattices. This waves take the form of light clusters that may fill an arbitrary number of lattice sites. We have demonstrated by numerical simulations that stable…
Phonon polaritons (PhPs) are hybrid light-matter modes. We investigate them in two-dimensional (2D) materials with twisted moir\'{e} structures, revealing that the moir\'{e} potential creates a new class of `moir\'{e} PhPs'. These exhibit a…
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…
The subject of the work is the stabilization of two-dimensional (2D) two-component (vector) solitons, in media with the attractive cubic nonlinearity, against the collapse by a linear lattice (LL, which is induced by a periodic modulation…
We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. Among the families of trapped beams are…
We report the first prediction of fully localized two-dimensional embedded solitons. These solitons are obtained in a quasi-one-dimensional waveguide array which is periodic along one spatial direction and localized along the orthogonal…
This article offers a review of results for solitons in 2D and 3D models of nonlinear dissipative media. The existence of such solitons requires to maintain two balances: between nonlinear self-focusing and linear diffraction and/or…
A review is given of some well-known and some recent results for two- and three-dimensional (2D and 3D) solitons, with emphasis on states carrying embedded vorticity. Unlike typically stable 1D solitons, 2D and 3D ones are vulnerable to…
Various families of charge-one vortex solitons in two-dimensional periodic media are reported. These vortices reside either in the semi-infinite gap or higher band gaps of the media. For both Kerr and saturable nonlinearities (either…
We report results of systematic numerical studies of 2D matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution…
Vortex solitons (dark solitons) are described in self-defocusing Kerr media whose phase line singularity is not parallel to the propagation direction, but is perpendicular or tilted almost arbitrary angles, depending on the medium linear…
Discrete fundamental and dipole solitons are constructed, in an exact analytical form, in an array of linear waveguides with an embedded $\mathcal{PT}$-symmetric dimer, which is composed of two nonlinear waveguides carrying equal gain and…
Plasmons in low-dimensional systems respresent an important tool for coupling energy into nanostructures and the localization of energy on the scale of only a few nanometers. Contrary to ordinary surface plasmons of metallic bulk materials,…
Very narrow spatial bright solitons in (1+1)D and (2+1)D versions of cubic-quintic and full saturable models are studied, starting from the full system of the Maxwell's equations, rather than from the paraxial (NLS) approximation. For the…
We analytically study nonlinear quasi-monochromatic plasma waves in a two-dimensional electron system set between the two metal electrodes (gates). We derive a nonlinear Schrodinger equation for a slow-varying envelope to describe the…
We characterize the spatial optical solitons supported by arrays of metallic nanowires embedded in Kerr-type material. The array of nanowires is described using an effective medium model and is regarded as a continuous medium. It is shown…
We describe a new type of spatially periodic structure (lattice models): a polaritonic crystal (PolC) formed by a two-dimensional lattice of trapped two-level atoms interacting with quantised electromagnetic field in a cavity (or in a…