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In the hydrodynamic representation of a quantum fluid or optical field, vorticity vanishes wherever the phase is well defined, and is instead localized at phase singularities, or quantum vortices. Pseudovorticity, by contrast, characterizes…
We introduce a system of propagation equations for the fundamental-frequency (FF) and second-harmonic (SH) waves in the bulk waveguide with the effective fractional diffraction and quadratic (chi ^(2)) nonlinearity. The numerical solution…
Instabilities are predicted for a sufficiently long hollow photonic optical fiber, or "cavity", containing a one dimensional Bose-gas in the presence of a classical, far red-detuned, confined weak electromagnetic mode. We examine both a…
We predict that a photon condensate inside a dye-filled microcavity forms long-lived spatial structures that resemble vortices when incoherently excited by a focused pump orbiting around the cavity axis. The finely structured density of the…
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 consider two self-dual abelian Higgs systems obtained from Lorentz breaking symmetry models by dimensional reduction. For the first model, we show that the self-dual equations are identical to those of Nielsen-Olesen vortices. Also, we…
We report the first observation of robust self-trapping of vortex beams propagating in a uniform condensed medium featuring local saturable self-focusing nonlinearity. Optical vortices with topological charge m=1, that remain self-trapped…
Two-dimensional spatial solitonic lattices are generated and investigated experimentally and numerically in an SBN:Ce crystal. An enhanced stability of these lattices is achieved by exploiting the anisotropy of coherent soliton interaction,…
Discrete fundamental and dipole solitons are constructed, in an exact analytical form, in an array of linear waveguides with an embedded $\mathcal{PT}$-symmetric dimer, which is composed of two nonlinear waveguides carrying equal gain and…
We study spatial and temporal solitons in the $\mathcal{PT}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single…
We investigate the properties of single vortices and of vortex lattice in a rotating dipolar condensate. We show that vortices in this system possess many novel features induced by the long-range anisotropic dipolar interaction between…
We carry out a detailed stability analysis of the superconducting vortex solutions in the Weinberg-Salam theory described in Nucl.Phys. B826 (2010) 174. These vortices are characterized by constant electric current $I$ and electric charge…
We propose a method for achieving dynamically controllable transport of highly mobile matter-wave solitons in a driven two-dimensional optical lattice. Our numerical analysis based on the mean-field model and the theory based on the…
Superconductors have two key characteristics. They expel magnetic field and they conduct electrical current with zero resistance. However, both properties are compromised in high magnetic fields which can penetrate the material and create a…
At low temperatures and 3He concentrations below 6.6 %, there is experimental evidence about the existence in liquid helium mixtures, of stable vortices with 3He-rich cores. When the system is either supersaturated or submitted to a tensile…
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…
The three-dimensional stability problem of a stretched stationary vortex is addressed in this letter. More specifically, we prove that the discrete part of the temporal spectrum is only associated with two-dimensional perturbations.
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
Stable vortex solitons (VSs) are objects of great interest for fundamental studies and various applications, including particle trapping, microscopy, data encoding, and matter-wave gyroscopes. However, three-dimensional (3D) VSs with high…
In this study, we investigate the existence and stability of in-phase and out-of-phase dissipative solitons in a dual-waveguide lattice with linear localized gain and nonlinear losses under both focusing and defocusing nonlinearities.…