Related papers: Vortex modes supported by spin-orbit coupling in a…
We study coupled unstaggered-staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schr\"{o}dinger (DNLS) equations with the self-attractive on-site self-phase-modulation nonlinearity, coupled by the repulsive…
It is known that, in continuous media, composite solitons with hidden vorticity, which are built of two mutually symmetric vortical components whose total angular momentum is zero, may be stable while their counterparts with explicit…
Symbiotic vortex-bright soliton structures with non-trivial topological charge in one component are found to be robust in immiscibel two-component superfluids, due to the effective potential created by a stable vortex in the other…
We explore a prototypical two-dimensional model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis,…
A recent analysis has revealed singular but physically relevant 2D localized vortex states with density ~ 1/r^{4/3} at r --> 0 and a convergent total norm, which are maintained by the interplay of the potential of the attraction to the…
We elaborate two generic methods for producing two-dimensional (2D) spatial soliton arrays (SSAs) in the framework of the cubic-quintic (CQ) complex Ginzburg-Landau (CGL) model. The first approach deals with a broad beam launched into the…
The form and stability properties of axisymmetric and spherically symmetric stationary states in two and three dimensions, respectively, are elucidated for Bose-Einstein condensates. These states include the ground state, central vortices,…
By means of the variational method and numerical simulations, we demonstrate the existence of stable 3D nonlinear modes, viz. vortex ``bullets'', in the form of pulsed beams carrying orbital angular momentum, that can self-trap in a 2D…
It is known that optical-lattice (OL) potentials can stabilize solitons and solitary vortices against the critical collapse, generated by the cubic attractive nonlinearity in the 2D geometry. We demonstrate OLs can also stabilize various…
We report results of systematic numerical analysis of collisions between two and three stable dissipative solitons in the two-dimensional (2D) complex Ginzburg- Landau equation (CGLE) with the cubic-quintic (CQ) combination of gain and loss…
Dissipative vortices are stable two-dimensional localized structures existing due to balance between gain and loss in nonlinear systems far from equilibrium. Being resistant to the dispersion and nonlinear distortions they are considered as…
We consider a two-component, two-dimensional nonlinear Schr\"{o}dinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a…
By using ZEUS cluster at Embry-Riddle Aeronautical University we perform extensive numerical simulations based on a two-dimensional Fourier spectral method Fourier spatial discretization and an explicit scheme for time differencing) to find…
We introduce a model of a two-core system, based on an equation of the Ginzburg-Landau (GL) type, coupled to another GL equation, which may be linear or nonlinear. One core is active, featuring intrinsic linear gain, while the other one is…
We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light…
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 numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers. In the distributed model (complex cubic-quintic Ginzburg-Landau equation) we observe a discrete family of soliton pairs with…
It is shown that the pair plasmas with small temperature asymmetry can support existence of localized as well as de-localized optical vortex solitons. Coexistence of such solitons is possible due to peculiar form of saturating nonlinearity…
The subject of the work is the stabilization of two-dimensional (2D) two-component (vector) solitons, in media with the attractive cubic nonlinearity, against the collapse by a linear lattice (LL, which is induced by a periodic modulation…
We report solutions for stable compound solitons in a three-dimensional quasi-phase-matched photonic crystal with the quadratic ($\chi ^{(2)}$) nonlinearity. The photonic crystal is introduced with a checkerboard structure, which can be…