Related papers: Stable Vortex Solitons in Nonlocal Self-Focusing N…
We show that surface solitons in the one-dimensional nonlinear Schr\"odinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel…
We consider the impact of anisotropic nonlocality on the arrest of the collapse and stabilization of dipole-mode (DM) solitons in two-dimensional (2D) models of optical media with the diffusive nonlinearity. The nonlocal nonlinearity is…
We predict that nonlinear left-handed metamaterials can support both TE- and TM-polarized self-trapped localized beams, spatial electromagnetic solitons. Such solitons appear as single- and multi-hump beams, being either symmetric or…
The article summarizes the studies of wave fields in structured non-equilibrium media describing by means of nonlocal hydrodynamic models. Due to the symmetry properties of models, we derived the invariant wave solutions satisfying…
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 report on the existence and stability of multidimensional bound solitonic states in harmonically-trapped scalar Bose-Einstein condensates. Their equilibrium separation, as a measure of the strength of the soliton-soliton or the solitonic…
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…
We report analytical solutions for spatial solitons supported by layers of a quadratically nonlinear material embedded into a linear planar waveguide. A full set of symmetric, asymmetric, and antisymmetric modes pinned to a symmetric pair…
We put forward new properties of lattice solitons in materials and geometries where both, the linear refractive index and the nonlinearity are spatially modulated. We show that the interplay between linear and out-of-phase nonlinear…
We prove a sufficient condition for nonlinear stability of relative equilibria in the planar $N$-vortex problem. This result builds on our previous work on the Hamiltonian formulation of its relative dynamics as a Lie--Poisson system. The…
This paper concerns the stabilizing effect of viscosity on the vortex sheets. It is found that although a vortex sheet is not a time-asymptotic attractor for the compressible Navier-Stokes equations, a viscous wave that approximates the…
We study theoretically the spatial evolution of optical beams inside a graded-index fiber exhibiting saturable nonlinearity. Utilizing an approach based on the variational principle, we identify the existence of bistable spatial solitons…
We investigate the propagation of the spatial soliton in cylindrical strongly nonlocal media by a novel method of image beam of light. The effect of the boundary on the soliton acting as the dynamic force for the soliton steering is…
The optical spatial solitons with ellipse-shaped spots have generally been considered to be a result of either linear or nonlinear anisotropy. In this paper, we introduce a class of spiraling elliptic solitons in the nonlocal nonlinear…
In this paper, we propose a numerical framework to study the shapes, dynamics and the stabilities of the self-localized solutions of the nonlinear wave blocking problem. With this motivation, we use the nonlinear Schr\"odinger equation…
It is shown that delocalized vortex solitons in relativistic pair plasmas with small temperature asymmetries can be unstable for intermediate intensities of the background electromagnetic field. Instability leads to the generation of…
We investigate the existence and stability of three-dimensional (3D) solitons supported by cylindrical Bessel lattices (BLs) in self-focusing media. If the lattice strength exceeds a threshold value, we show numerically, and using the…
By means of variational methods and systematic numerical analysis, we demonstrate the existence of stable solitons in three-dimensional (3D) free space, in the context of binary atomic condensates combining contact self-attraction and…
We present a numerical solution in the form of a three-dimensional (3D) vortex soliton in unmagnetized plasma in the model of the generalized Zakharov equations with saturating exponential nonlinearity. To find the solution with a high…
The nonlinear lattice---a new and nonlinear class of periodic potentials---was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic…