Related papers: Gap solitons on a ring
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 study two-dimensional (2D) matter-wave gap solitons trapped in an elliptically deformed concentric lattice potential, within the framework of the Gross-Pitaevskii equation (GPE) with self-attraction or self-repulsion. For a fixed…
We address the formation of topological edge solitons in rotating Su-Schrieffer-Heeger waveguide arrays. The linear spectrum of the non-rotating topological array is characterized by the presence of topological gap with two edge states…
As is known, a solitary pulse in the complex cubic Ginzburg-Landau (GL) equation is unstable. We demonstrate that a system of two linearly coupled GL equations with gain and dissipation in one subsystem and pure dissipation in another…
We show that the geometrically-induced potential existing in undulated slab waveguides dramatically affects the properties of solitons. In particular, whereas solitons residing in the potential maxima do not feature power thresholds and are…
The stability of two-dimensional bright vortex solitons in a media with focusing cubic and defocusing quintic nonlinearities is investigated analytically and numerically. It is proved that above some critical beam powers not only one- and…
We propose a new type of topological states of matter exhibiting topologically nontrivial edge states (ESs) within gapless bulk states (GBSs) protected by both spin rotational and reflection symmetries. A model presenting such states is…
Ring dark and anti-dark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable continuous-wave background, and exist in a weak or strong nonlocality regime, defined by…
We consider a one-dimensional model of a two-component Bose-Einstein condensate in the presence of periodic external potentials of opposite signs, acting on the two species. The interaction between the species is attractive, while…
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,…
We study the excitations of dark solitons in a nonlinear optical fiber with the second- and fourth-order dispersion, and find the emergence of striped dark solitons (SDSs) and some multi-dark-soliton bound states. The SDSs can exhibit…
We investigate one-dimensional charge conserving, spin-singlet (SSS) and spin-triplet (STS) superconductors in the presence of boundary fields. In systems with Open Boundary Conditions (OBC) it has been demonstrated that STS display a…
The resonant scattering of gap solitons (GS) of the periodic nonlinear Schr\"odinger equation with a localized defect which is symmetric under the parity and the time-reversal (PT) symmetry, is investigated. It is shown that for suitable…
Two-dimensional (2D) equations describing the nonlinear interaction between upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal nonlinearity in the equations results in the possibility of existence of stable 2D nonlinear…
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…
By means of a systematic numerical analysis, we demonstrate that hexagonal lattices of parallel linearly-coupled waveguides, with the intrinsic cubic self-focusing nonlinearity, give rise to three species of stable semi-discrete complexes…
We introduce partially-parity-time-symmetric (pPT-symmetric) azimuthal potentials composed from individual PT-symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potentials excitations…
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…
Our analysis suggests strongly that stationary pulses exist in nonlinear media with second-, third-, and fourth-order dispersion. A theory, based on the variational approach, is developed for finding approximate parameters of such solitons.…
We study stationary rotating topological solitons in (2+1)-dimensional ${\mathbb C}P^2$ non-linear sigma model with a stabilizing potential term. We find families of $U(1)\times U(1)$ symmetric solutions with topological degrees larger than…