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Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were…

A suitable correction of the Maxwell model brings to an enlargement of the space of solutions, allowing for the existence of solitons in vacuum. We review the basic achievements of the theory and discuss some approximation results based on…

We consider the ultrashort light pulse propagation through an inhomogeneous monomodal optical fiber exhibiting higher-order dispersive effects. Wave propagation is governed by a generalized nonlinear Schr\"{o}dinger equation with varying…

We demonstrate experimentally and numerically the existence spatial solitons in multiple-quantum-well semiconductor microresonators driven by an external coherent optical field. We discuss stability of the semiconductor-resonator solitons…

Unidirectional reflectionless propagation (or transmission) is an interesting wave phenomenon observed in many $\mathcal{PT}$-symmetric optical structures. Theoretical studies on unidirectional reflectionless transmission often use simple…

We suggest a novel type of composite spatial optical soliton created by a coherent vortex beam guiding a partially incoherent light beam in a self-focusing nonlinear medium. We show that the incoherence of the guided mode may enhance,…

Solitons are localized nonlinear wave packets that propagate without spreading because nonlinearity balances dispersion. Their robustness is well understood in effectively one-dimensional systems, but introducing additional spatial…

We study spatial optical solitons in a one-dimensional nonlinear photonic crystal created by an array of thin-film nonlinear waveguides, the so-called Dirac-comb nonlinear lattice. We analyze modulational instability of the extended…

We address the properties of surface solitons supported by optical lattices imprinted in photorefractive media with asymmetric diffusion nonlinearity. Such solitons exist only in finite gaps of lattice spectrum. In contrast to latticeless…

In the hydrodynamic representation of a quantum fluid or optical field, vorticity vanishes wherever the phase is well defined, and is instead localized at phase singularities, or quantum vortices. Pseudovorticity, by contrast, characterizes…

We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light…

Interactions of noncommutative waves and solitons in 2+1 dimensions can be analyzed exactly for a supersymmetric and integrable U(n) chiral model extending the Ward model. Using the Moyal-deformed dressing method in an antichiral…

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 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…

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…

We explore the problem of scattering in a medium modulated by a superluminal rectangular pulse, with the pulse modulation realized through transverse excitations. We solve this problem in the moving frame where the modulation appears purely…

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 theoretically show the existence of cascaded second-order surface plasmon solitons propagating at the interface between metal and linear dielectric. Nonlocal multipole nonlinearities originating from free conduction electron plasma of a…

We introduce a model of media with the cubic attractive nonlinearity concentrated along a single or double stripe in the two-dimensional (2D) plane. The model can be realized in terms of nonlinear optics (in the spatial and temporal domains…

Multi-dimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial…