Related papers: Localized modes in $\chi^{(2)}$ media with $\PT$-s…
We consider two-component solitons in a medium with a periodic modulation of the nonlinear coefficient. The modulation enables the existence of complex multihump vector states. In particular, vector solitons composed of dipole and…
The stability of two-dimensional bright vortex solitons in a media with focusing cubic and defocusing quintic nonlinearities is investigated analytically and numerically. It is proved that above some critical beam powers not only one- and…
We introduce the notion of a ${\cal PT}$-symmetric dimer with a $\chi^{(2)}$ nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and…
We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its…
The effect of finite boundaries in the propagation of spatial nonlocal solitons in media with cylindrical symmetry is analyzed. Using Ehrenfest's theorem together with the Green's function of the nonlinear refractive index equation, we…
It is well known that a symmetric soliton in coupled nonlinear Schroedinger (NLS) equations with the cubic nonlinearity loses its stability with the increase of its energy, featuring a transition into an asymmetric soliton via a subcritical…
It is studied the bright spatial solitons in nonlocal defocusing Kerr media with parity-time (PT) symmetric potentials. We find that these solitons can exist and be stable over a different range of potential parameters. The influence of the…
We consider settings providing the existence of stable two-dimensional (2D) dissipative solitons with zero and nonzero vorticity in optical media with the quadratic ($\chi^{(2)}$) nonlinearity. To compensate the spatially uniform loss in…
We study the bound states of two-dimensional bright solitons in nonlocal nonlinear media. The general properties and stability of these multisolitary structures are investigated analytically and numerically. We have found that a steady…
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 report families of discrete optical solitons in frequency space, or spectral-discrete solitons existing in a dispersive Raman medium, where individual side-bands are coupled by coherence. The associated time-domain patterns correspond to…
A modification of the usual Type-II second-harmonic-generation model is proposed, which includes two additional features: linear conversion and walkoff (group-velocity difference) between two components of the fundamental-frequency (FF)…
We address the stabilization of dipole solitons in nonlocal nonlinear materials by two different approaches. First, we study the properties of such solitons in thermal nonlinear media, where the refractive index landscapes induced by laser…
Stability is an essential problem in theoretical and experimental studies of solitons in nonlinear media with fractional diffraction, which is represented by the Riesz derivative with Levy index (LI) taking values LI < 2. Fractional…
We investigate branched PT-symmetric optical lattices. We consider both the linear and nonlinear Schr\"odinger equations with a PT-symmetric periodic potential on the graph and solve them by imposing weighted vertex boundary conditions. A…
We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schr\"odinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the…
Dynamics of symmetric and antisymmetric 2-solitons and 3-solitons is studied in the model of the nonlinear dual-core coupler and its PT-symmetric version. Regions of the convergence of the injected perturbed symmetric and antisymmetric…
We report on detailed investigation of the stability of localized modes in the nonlinear Schrodinger equations with a nonlinear parity-time (alias PT) symmetric potential. We are particularly focusing on the case where the…
Our analysis suggests strongly that stationary pulses exist in nonlinear media with second-, third-, and fourth-order dispersion. A theory, based on the variational approach, is developed for finding approximate parameters of such solitons.…
We derive for the first time fundamental equations that describe soliton spatial profiles consisting of two-photon mode fields and macroscopic polarization of medium. Numerical solutions of this basic equation are presented to give single…