Related papers: Quantum Solitons with Cylindrical Symmetry
We consider the nonlinear Schr\"odinger equation with a focusing cubic term and a defocusing quintic nonlinearity in dimensions two and three. The core of this article is the notion of stability of solitary waves. We recall the two standard…
In recent work, several classes of solitonic solutions of string theory with higher-membrane structure have been obtained. These solutions can be classified according to the symmetry possessed by the solitons in the subspace of the…
We study the formation of spin-1 symbiotic spinor solitons in a quasi-one- (quasi-1D) and quasi-two-dimensional (quasi-2D) hyper-fine spin $F=1$ ferromagnetic Bose-Einstein condensate (BEC). The symbiotic solitons necessarily have a…
We demonstrate that modulation of the local strength of the cubic self-focusing (SF) nonlinearity in the two-dimensional (2D) geometry, in the form of a circle with contrast $\Delta g$ of the SF coefficient relative to the ambient medium…
Topological objects resulting from symmetry breakdown may be either stable or metastable depending on the pattern of symmetry breaking. However, if they acquire zero-energy modes of fermions, and in the process acquire non-integer fermionic…
We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…
We introduce a novel class of parametric optical solitons supported simultaneously by two second-order nonlinear cascading processes, second-harmonic generation and sum-frequency mixing. We obtain, analytically and numerically, the…
We consider possibilities to control dynamics of solitons of two types, maintained by the combination of cubic attraction and spin-orbit coupling (SOC) in a two-component system, namely, semi-dipoles (SDs) and mixed modes (MMs), by making…
Classical Heisenberg spins in the continuum limit (i.e. the nonlinear sigma-model) are studied on an elastic cylinder section with homogeneous boundary conditions. The latter may serve as a physical realization of magnetically coated…
We investigate bright matter-wave solitons in the presence of a spatially varying nonlinearity. It is demonstrated that a translation mode is excited due to the spatial inhomogeneity and its frequency is derived analytically and also…
In the strictly periodic setting, the electric polarization of inversion-symmetric solids with and without time-reversal symmetry and the isotropic magneto-electric response function of time-reversal symmetric insulators are known to be…
Recent results suggest that multi-Skyrmions stabilized by omega mesons have very similar properties to those stabilized by the Skyrme term. In this paper we present the results of a detailed numerical investigation of a (2+1)-dimensional…
We introduce one- and two-dimensional (1D and 2D) models of parity-time ($% \mathcal{PT}$) -symmetric couplers with the mutually balanced linear gain and loss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting in each one.…
We describe a general N-solitonic solution of the focusing NLSE in the presence of a condensate by using the dressing method. We give the explicit form of one- and two- solitonic solutions and study them in detail. We distinguish a special…
In this paper we present soliton solutions of two coupled nonlinear Schodinger equations modulated in the bspace and time. The approach allows us to obatin solitons with large variety of solutions depending on the nonlinearity and the…
In this paper we present several set of solutions of static and spherically symmetric solitonic boson stars. Each set is characterized by the value of {\sigma} that defines the solitonic potential in the complex scalar field theory. The…
We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of breathers with high power. Three main regimes are observed:…
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…
Analytically solvable models are benchmarks in studies of phase transitions and pattern-forming bifurcations. Such models are known for phase transitions of the second kind in uniform media, but not for localized states (solitons), as…
We numerically investigate a particular type of spin solitons inside a trapped atomic spin-1 Bose-Einstein condensate (BEC) with ferromagnetic interactions. Within the mean field theory approximation, our study of the solitonic dynamics…