Related papers: Vortex-soliton complexes in coupled nonlinear Schr…
We consider evolution of one-dimensional nonlinear-Schr\"odinger (NLS) two-soliton complexes (breathers) with narrow repulsive or attractive potentials (barrier or well, respectively). By means of systematic simulations, we demonstrate that…
It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when…
We consider a two-dimensional (2D) two-component spinor system with cubic attraction between the components and intra-species self-repulsion, which may be realized in atomic Bose-Einstein condensates, as well as in a quasi-equilibrium…
In the present work we explore features of single and pairs of solitary waves in a fractional variant of the nonlinear Schr{\"o}dinger equation. Motivated by the recent experimental realization of arbitrary fractional exponents, upon…
The dynamics of a two-dimensional vortex are analyzed within the framework of the nonlinear Schrodinger equation. Both a bare vortex and a vortex with an external mass trapped in a finite-sized core are considered. The bare vortex motion is…
Periodic potentials with flat bands in their spectra support strongly localized nonlinear excitations. Although a perfectly flat band cannot exist in a continuous system, a spin-orbit-coupled Bose-Einstein condensate loaded in a Zeeman…
We reveal that spatially localized vortex solitons become stable in self-focusing nonlinear media when the vortex symmetry-breaking azimuthal instability is eliminated by a nonlocal nonlinear response. We study the main properties of…
We propose an integrable system of coupled nonlinear Schrodinger equations with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short optical soliton pulse propagation in non-Kerr media. Lax pair, conserved…
We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a…
The small dispersion limit of the focusing nonlinear Schrodinger equation with periodic initial conditions is studied analytically and numerically. First, through a comprehensive set of numerical simulations, it is demonstrated that…
We study the dynamics of fundamental and vortex solitons in the framework of the nonlinear Schr\"{o}dinger equation with the spatial dimension $D\geqslant 2$ with a multiplicative random term depending on the time and space coordinates. To…
The nonlinear Schr{\"o}dinger equation with derivative cubic nonlinearity admits a family of solitons, which are orbitally stable in the energy space. In this work, we prove the orbital stability of multi-solitons configurations in the…
We investigate stability the dynamical properties of one-dimensional interwires polar soliton molecules in a biwire setup with dipole moments aligned perpendicularly to the line of motion and in opposite directions in different wires.…
We study the dynamics of solitons under the action of one-dimensional quasiperiodic lattice potentials, fractional diffraction, and nonlinearity. The formation and stability of the solitons is investigated in the framework of the fractional…
We report on the existence and stability of multidimensional bound solitonic states in harmonically-trapped scalar Bose-Einstein condensates. Their equilibrium separation, as a measure of the strength of the soliton-soliton or the solitonic…
We construct families of ordinary and gap solitons (GSs), including solitary vortices, in the two-dimensional (2D) system based on the nonlinear-Schr\"Aodinger/Gross-Pitaevskii equation with the 2D or quasi-1D (Q1D) periodic linear…
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…
We consider the propagation of wave packets for a nonlinear Schr\"odinger equation, with a matrix-valued potential, in the semi-classical limit. For a matrix-valued potential, Strichartz estimates are available under long range assumptions.…
We study stability and dynamics of the single cylindrically symmetric solitary structures and dipolar solitonic molecules in spatially nonlocal media. The main properties of the solitons, vortex solitons, and dipolar solitons are…
We investigate the existence and especially the linear stability of single and multiple-charge quantized vortex states of nonlinear Schroedinger equations in the presence of a periodic and a parabolic potential in two spatial dimensions.…