Related papers: Two - dimensional solitons in media with the strip…
Recent studies have demonstrated that defocusing cubic nonlinearity with local strength growing from the center to the periphery faster than $r^{D}$, in space of dimension $D$ with radial coordinate $r$, supports a vast variety of robust…
The formation of unstaggered localized modes in dynamical lattices can be supported by the interplay of discreteness and nonlinearity with a finite relaxation time. In rapidly responding nonlinear media, on-site discrete solitons are…
The creation of stable 1D and 2D localized modes in lossy nonlinear media is a fundamental problem in optics and plasmonics. This article gives a short review of theoretical methods elaborated for this purpose, using localized gain applied…
We analyze a system of three two-dimensional nonlinear Schr\"odinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time…
We study quadratic solitons supported by two- and three-wave parametric interactions in chi-2 nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, 'almost exact', explicit analytical solutions,…
Assume a lower-dimensional solitonic structure embedded in a higher dimensional space, e.g., a 1D dark soliton embedded in 2D space, a ring dark soliton in 2D space, a spherical shell soliton in 3D space etc. By extending the Landau…
We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its…
Two-dimensional (2D) fundamental soliton-soliton pairs are investigated in binary mixtures of Bose-Einstein condensates with attractive interactions between atoms of the same type. Both attractive and repulsive interactions between atoms of…
We consider soliton solutions of a two-dimensional nonlinear system with the self-focusing nonlinearity and a quasi-1D confining potential, taking harmonic potential as an example. We investigate a single soliton in detail and find…
We introduce a 2D network built of $\mathcal{PT}$-symmetric dimers with on-site cubic nonlinearity, the gain and loss elements of the dimers being linked by parallel square-shaped lattices. The system may be realized as a set of…
We consider the three-dimensional (3D) mean-field model for the Bose-Einstein condensate (BEC), with a 1D nonlinear lattice (NL), which periodically changes the sign of the nonlinearity along the axial direction, and the harmonic-oscillator…
We consider possibilities to control dynamics of solitons of two types, maintained by the combination of cubic attraction and spin-orbit coupling (SOC) in a two-component system, namely, semi-dipoles (SDs) and mixed modes (MMs), by making…
The problem of the stability of solitons in second-harmonic-generating media with normal group-velocity dispersion (GVD) in the second-harmonic (SH) field, which is generic to available chi^(2) materials, is revisited. Using an iterative…
We address (2+1)D surface solitons occurring at the interface between a linear medium and a nonlocal nonlinear medium whose nonlinear contribution to the refractive index has a initial value at the interface. We find that there exist stable…
We present a new type of soliton solutions in nonlinear photonic systems with discrete point-symmetry. These solitons have their origin in a novel mechanism of breaking of discrete symmetry by the presence of nonlinearities. These so-called…
We investigate the stability properties of breather soliton trains in a three-dimensional Bose-Einstein Condensate with Feshbach Resonance Management of the scattering length. This is done so as to generate both attractive and repulsive…
We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the…
We reveal that lattice interfaces imprinted in nonlocal nonlinear media support surface solitons that do not exist in other similar settings, including interfaces of local and nonlocal uniform materials. We show the impact of nonlocality on…
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient…
We investigate fundamental localized modes in 2D lattices with an edge (surface). Interaction with the edge expands the stability area for ordinary solitons, and induces a difference between perpendicular and parallel dipoles; on the…