Related papers: Stabilization of solitons under competing nonlinea…
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 address the problem of existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of (2+1)-dimensional two-mode self-trapped beams, with…
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 consider a two-dimensional (2D) counterpart of the experiment that led to the creation of quasi-1D bright solitons in Bose-Einstein condensates (BECs) [Nature 417, 150--153 (2002)]. We start by identifying the ground state of the 2D…
We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schr\"{o}dinger equation (NLSE), which includes the harmonic-oscillator (HO) potential and a random potential. The…
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…
Stable self-trapped vortex annuli (VAs) with large values of topological charge S (giant VAs) are not only a subject of fundamental interest, but are also sought for various applications, such as quantum information processing and storage.…
We propose two models for the creation of stable dissipative solitons in optical media with the $\chi^{(2)}$ (quadratic) nonlinearity. To compensate spatially uniform loss in both the fundamental-frequency (FF) and second-harmonic (SH)…
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…
It was recently found that the spin-orbit (SO) coupling can help to create stable matter-wave solitons in spinor Bose-Einstein condensates in the two-dimensional (2D) free space. Being induced by external laser illumination, the effective…
Dynamical and self-trapping properties of two-dimensional (2D) binary mixtures of Bose-Einstein condensates (BECs) in cross-combined lattices consisting of a one-dimensional (1D) linear optical lattice (LOL) in the $x-$ direction for the…
In this letter we introduce the concept of stabilized vector solitons as nonlinear waves constructed by addition of mutually incoherent Townes solitons that are stabilized under the effect of a periodic modulation of the nonlinearity. We…
We study stability of solitary vortices in the two-dimensional trapped Bose-Einstein condensate (BEC) with a spatially localized region of self-attraction. Solving the respective Bogoliubov-de Gennes equations and running direct simulations…
We introduce a three-dimensional (3D) model of optical media with the quadratic ($\chi ^{(2)}$) nonlinearity and an effective 2D isotropic harmonic-oscillator (HO) potential. While it is well known that 3D \chi^2 solitons with embedded…
We consider two-dimensional (2D) localized vortical modes in the three-wave system with the quadratic ($\chi ^{(2)}$) nonlinearity, alias nondegenerate second-harmonic-generating system, guided by the isotropic harmonic-oscillator (HO)…
We introduce a system combining the quadratic self-attractive or composite quadratic-cubic nonlinearity, acting in the combination with the fractional diffraction, which is characterized by its L\'{e}vy index $\alpha $. The model applies to…
We propose a new mechanism for stabilization of confined modes in lasers and semiconductor microcavities holding exciton-polariton condensates, with spatially uniform linear gain, cubic loss, and cubic self-focusing or defocusing…
The existence, stability and other dynamical properties of a new type of multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional (1D or 2D, respectively) periodic potential in the nonlinear Schr\"{o}dinger equation…
We address the existence and properties of one-dimensional solitons maintained by localized parameter gain in focusing and defocusing lossy nonlinear media. Localized parametric gain supports both fundamental and multipole solitons. We…
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…