Related papers: High-Order-Mode Soliton Structures in Two-Dimensio…
We observe experimentally higher-order solitons in waveguide arrays with defocusing saturable nonlinearity. Such solitons can comprise several in-phase bright spots and are stable above a critical power threshold. We elucidate the impact of…
This concise review aims to provide a summary of the most relevant recent experimental and theoretical results for solitons, i.e., self-trapped bound states of nonlinear waves, in two- and three-dimensional (2D and 3D) media. In comparison…
We present a brief overview of the basic concepts of the soliton stability theory and discuss some characteristic examples of the instability-induced soliton dynamics, in application to spatial optical solitons described by the NLS-type…
We consider an array of double oligomers in an optical waveguide device. A mathematical model for the system is the coupled discrete nonlinear Schr\"odinger (NLS) equations, where the gain-and-loss parameter contributes to the…
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…
In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear Schr{\"{o}}dinger equation, we find discrete vortex solitons with various values of the topological charge $S$. Stability regions for the vortices with…
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 properties of the localized states of a two component Bose-Einstein condensate confined in a nonlinear periodic potential [nonlinear optical lattice] are investigated. We reveal the existence of new types of solitons and study their…
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.…
Two-dimensional (2D) equations describing the nonlinear interaction between upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal nonlinearity in the equations results in the possibility of existence of stable 2D nonlinear…
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with low-dimensional (1D) conservative plus dissipative nonlinear optical lattices are investigated. In the case of focusing media (with attractive…
We introduce discrete multivortex solitons in a ring of nonlinear oscillators coupled to a central site. Regular clusters of discrete vortices appear as a result of mode collisions and we show that their stability is determined by global…
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 propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly…
We study the existence and stability of localized states in the discrete nonlinear Schr{\"o}dinger equation (DNLS) on two-dimensional non-square lattices. The model includes both the nearest-neighbor and long-range interactions. For the…
We report on the frst experimental observation of discrete vortex solitons in two-dimensional optically-induced photonic lattices. We demonstrate strong stabilization of an optical vortex by the lattice in a self-focusing nonlinear medium…
We report on the existence and stability of multicolor lattice vortex solitons constituted by coupled fundamental frequency and second-harmonic waves in optical lattices in quadratic nonlinear media. It is shown that the solitons are stable…
We report that infinite and semi-infinite lattices with spatially inhomogeneous self-defocusing (SDF)\ onsite nonlinearity, whose strength increases rapidly enough toward the lattice periphery, support stable unstaggered (UnST) discrete…
Stable ring vortex solitons, featuring a bright-shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice.…
We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active defocusing media, where the gain exceeds damping in the low-amplitude limit. A…