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By means of systematic simulations we demonstrate generation of a variety of ring-shaped optical vortices (OVs) from a two-dimensional input with embedded vorticity, in a dissipative medium modeled by the cubic-quintic complex…
We introduce a model of a lossy second-harmonic-generating (chi^2) cavity externally pumped at the third harmonic, which gives rise to driving terms of a new type, corresponding to a cross-parametric gain. The equation for the…
We put forward a model for trapping stable optical vortex solitons (VSs) with high topological charges $m$. The cubic-quintic nonlinear medium with an imprinted ring-shaped modulation of the refractive index is shown to support two branches…
We construct a variety of novel localized states with distinct topological structures in the 3D discrete nonlinear Schr{\"{o}}dinger equation. The states can be created in Bose-Einstein condensates trapped in strong optical lattices, and…
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…
We predict the existence of spatially localized nontrivial vortex states of a Bose-Einstein condensate with repulsive atomic interaction confined by a three-dimensional optical lattice. Such vortex-like structures include planar vortices,…
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…
Solitons in the fractional space, supported by lattice potentials, have recently attracted much interest. We consider the limit of deep one- and two-dimensional (1D and 2D) lattices in this system, featuring finite bandgaps separated by…
We address the existence, stability, and evolution of two-dimensional vortex quantum droplets (VQDs) in binary Bose-Einstein condensates trapped in a ring-shaped potential. The interplay of the Lee-Huang-Yang-amended nonlinearity and…
We develop stability analysis for matter-wave solitons in a two-dimensional (2D) Bose-Einstein condensate loaded in an optical lattice (OL), to which periodic time modulation is applied, in different forms. The stability is studied by dint…
In this paper, we consider the dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schroedinger model, a model of interest both to atomic physics and to nonlinear optics. We find that in a way…
In this work we study spherical shell dark soliton states in three-dimensional atomic Bose-Einstein condensates. Their symmetry is exploited in order to analyze their existence, as well as that of topologically charged variants of the…
We address the dynamics of two-dimensional (2D) truncated Airy waves and three-component solitons in the system of two fundamental-frequency and second-harmonic fields, coupled by quadratic (chi^(2)) terms. The system models…
The existence and stability of solitons in Bose-Einstein condensates with attractive inter-atomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic…
The form and stability properties of axisymmetric and spherically symmetric stationary states in two and three dimensions, respectively, are elucidated for Bose-Einstein condensates. These states include the ground state, central vortices,…
Using group theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition…
We study the stability of the vortex in a 2D model of continuous compressible media in a uniformly rotating reference frame. As it is known, the axisymmetric vortex in a fixed reference frame is stable with respect to asymmetric…
We demonstrate that families of vortex solitons are possible in a bi-dispersive three-dimensional nonlinear Schrodinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third…
We elaborate one- and two-dimensional (1D and 2D) models of media with self-repulsive cubic nonlinearity, whose local strength is subject to spatial modulation that admits the existence of flat-top solitons of various types, including…
This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history. Some findings, such as optical solitons supported by thermal nonlinearity, and by the orientational nonlinearity…