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It is known that the interplay of the spin-orbit-coupling (SOC) and mean-field self-attraction creates stable two-dimensional (2D) solitons (ground states) in spinor Bose-Einstein condensates. However, SOC destroys the system's Galilean…
Condensation of exciton-polaritons has been recently observed in one-dimensional photonic crystal waveguides, exploiting the interplay of long-lived gap confined eigenmodes and negative mass polariton branches. Here we focus on the…
We show that the balance between localized gain and nonlinear cubic dissipation in the twodimensional nonlinear Schrodinger equation allows for existence of stable two-dimensional localized modes which we identify as solitons. Such modes…
Fundamental and vortex solitons in a two-dimensional optically induced waveguide array are reported. In the strong localization regime, the fundamental soliton is largely confined to one lattice site, while the vortex state comprises of…
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 report on the frst experimental observation of discrete vortex solitons in two-dimensional optically-induced photonic lattices. We demonstrate strong stabilization of an optical vortex by the lattice in a self-focusing nonlinear medium…
We theoretically investigate the excitation, dynamics of parametrically driven soliton crystals and their resulting frequency combs in doubly resonant cavities with quadratic and cubic nonlinearities. We demonstrate that soliton crystal…
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…
Optical modes of a multilayered photonic structure with the twisted nematic liquid crystal as a defect layer have been investigated. The electroconvective flow in the nematic makes a spatially periodic structure in the form of abnormal…
We propose a simple dissipative system with purely cubic defocusing nonlinearity and nonuniform linear gain that can support stable localized dissipative vortex solitons with high topological charges without the utilization of competing…
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…
We have developed an analytical model based on the perturbation theory in order to study the optical propagation of two successive intense solitons in hollow-core photonic crystal fibers filled with Raman-active gases. Based on the time…
A model of a Bose-Einstein condensate in a ring optical lattice with atomic dissipations applied at a stationary or at a moving location on the ring is presented. The localized dissipation is shown to generate and stabilize both stationary…
Temporal optical solitons have been the subject of intense research due to their intriguing physics and applications in ultrafast optics and supercontinuum generation. Conventional bright optical solitons result from the interaction of…
The light ray of a spatial soliton in an optical film whose refractive index is smoothly modulated (wavelength much larger than the typical soliton width) in both spatial directions is shown to possess chaotic regimes for which the…
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 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…
It is shown that three or more dark/gray solitons can form bound states in nonlocal media. More over dark/gray solitons can form bound states in several balance distances. Numerical simulations indicate that some of such bound states are…
We address the existence, stability, and propagation dynamics of multipole-mode solitons in cubic-quintic nonlinear media with an imprinted annular (ring-shaped) potential. The interplay of the competing nonlinearity with the potential…
Criteria for experimental observation of multi-dimensional optical solitons in media with saturable refractive nonlinearities are developed. The criteria are applied to actual material parameters (characterizing the cubic self-focusing and…