Related papers: Two-dimensional vector solitons stabilized by a li…
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…
Dipole and quadrupole solitons in a two-dimensional optically induced defocus- ing photonic lattice are theoretically predicted and experimentally observed. It is shown that in-phase nearest-neighbor dipole and out-of-phase…
We consider splitting and stabilization of second-order solitons (2-soliton breathers) in a model based on the nonlinear Schr\"{o}dinger equation (NLSE), which includes a small quintic term, and weak resonant nonlinearity management (NLM),…
We introduce vector soliton complexes in nonlocal Kerr-type nonlinear media. We discover that under proper conditions the combination of nonlocality and vectorial coupling has a remarkable stabilizing action on multi-humped solitons. In…
We address necklace solitons supported by circular waveguide arrays with out-of-phase modulation of nonlinearity and linear refractive index. Such two-dimensional necklace solitons appear as rings of multiple out-of-phase bright spots. We…
We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in…
Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice…
We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schroedinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities.…
We introduce one- and two-dimensional (1D and 2D) models of parity-time ($% \mathcal{PT}$) -symmetric couplers with the mutually balanced linear gain and loss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting in each one.…
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…
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…
We consider a two-dimensional nonlinear waveguide with distributed gain and losses. The optical potential describing the system consists of an unperturbed complex potential depending only on one transverse coordinate, i.e., corresponding to…
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 show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, give rise to completely localized spatiotemporal solitons (vortex tori) with vorticity…
We study two-dimensional soliton-soliton vector pairs in media with self-focusing nonlinearities and defocing cross-interactions. The general properties of the stationary states and their stability are investigated. The different scenarios…
We report stable composite vortex solitons in the model of a three-dimensional photonic crystal with the third-harmonic (TH) generation provided by the quasi-phase-matched quadratic nonlinearity. The photonic crystal is designed with a…
Existence, stability and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel 2D (two-dimensional) lattices, are investigated. The system with the on-site cubic self-focusing nonlinearity…
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 revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the two-dimensional (2D) cubic-quintic nonlinear Schr{\"o}dinger equation. We develop a semi-analytical approach,…
We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schr\"{o}dinger (DNLS) equations with the attractive self-phase-modulation (SPM) nonlinearity, coupled…