Related papers: Stability and dynamics of two-soliton molecules
We establish the stability in the energy space for sums of solitons of the one-dimensional Gross-Pitaevskii equation when their speeds are mutually distinct and distinct from zero, and when the solitons are initially well-separated and…
By numerical and variational analysis of the three-dimensional Gross-Pitaevskii equation we study the formation and dynamics of bright and vortex-bright solitons in a cigar-shaped dipolar Bose-Einstein condensate for large repulsive atomic…
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.…
Soliton dynamics in a large variety of longitudinally modulated lattices are studied in terms of phase space analysis for an effective particle approach and direct numerical simulations. Complex soliton dynamics are shown to depend strongly…
Analytic expressions have been derived for the interaction potential between dipolar bright solitons and the binding energy of a two-soliton molecule. The properties of these localized structures are explored with a focus on their behavior…
We investigate the dynamics of matter-wave solitons in the presence of a spatially varying atomic scattering length and nonlinearity. The dynamics of bright and dark solitary waves is studied using the corresponding Gross-Pitaevskii…
Dynamics of solitons of the Ablowitz-Ladik model in the presence of a random potential is studied. In absence of the random potential it is an integrable model and the solitons are stable. As a result of the random potential this stability…
We propose a method of forming matter-wave soliton molecules that is inspired by the recent experiment of Dris {\it et al.}. In the proposed set-up we show that if two solitons are initially prepared in phase and with a sufficiently small…
The bright matter wave soliton propagation through a barrier with a rapidly oscillating position is investigated. The averaged over rapid oscillations Gross-Pitaevskii (GP) equation is derived. It is shown that the soliton is dynamically…
In this paper we present some recent results concerning the ex- istence, the stability and the dynamics of solitons occurring in the nonlinear Schroedinger equation when the parameter h -> 0. We focus on the role played by the Energy and…
By introducing and solving two correlative constrained variational problems as well as spectrum analysis, an approach to fix soliton frequency from the prescribed mass for nonlinear Schr\"odinger equations is found, and an open problem in…
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statistically translation-invariant. We show that, for small…
Algebraic soliton interactions with a periodic or quasi-periodic random force are investigated using the Benjamin-Ono equation. The random force is modeled as a Fourier series with a finite number of modes and random phases uniformly…
Two-dimensional (2D) fundamental soliton-soliton pairs are investigated in binary mixtures of Bose-Einstein condensates with attractive interactions between atoms of the same type. Both attractive and repulsive interactions between atoms of…
We introduce a dynamical model of a Bose-Einstein condensate based on the 2D Gross-Pitaevskii equation, in which the nonlinear coefficient is a function of radius. The model describes a situation with spatial modulation of the negative…
The nonstationary dynamics of topological solitons (dislocations, domain walls, fluxons) and their bound states in one-dimensional systems with high dispersion are investigated. Dynamical features of a moving kink emitting radiation and…
We derive exact solitonic solutions of the one-dimensional time-dependent Gross-Pitaevskii equation with time-dependent strengths of the harmonic external potential and the interatomic interaction. The time-dependence of the external…
Two-component Bose-Einstein condensates in the miscible phase can support polarization solitary waves, known as magnetic solitons. By calculating the interaction potential between two magnetic solitons, we elucidate the mechanisms and…
By means of analytical and numerical methods, we study how the residual three-dimensionality affects dynamics of solitons in an attractive Bose-Einstein condensate loaded into a cigar-shaped trap. Based on an effective 1D Gross-Pitaevskii…
The small oscillations of solitons in 2D Bose-Einstein condensates are investigated by solving the Kadomtsev-Petviashvili equation which is valid when the velocity of the soliton approaches the speed of sound. We show that the soliton is…