Related papers: Dark solitons revealed in Lieb-Liniger eigenstates
Lieb-Liniger model describes bosons with contact interactions in one-dimensional space. In the limit of weak repulsive particle interactions, there are two types of low lying excitation spectrum. The first is reproduced by the Bogoliubov…
The thesis contains description of the Lieb-Liniger model in the context of the correspondence between dark solitons and the so-called hole excitations. We present a detailed analysis of the analytical solution given by the Bethe ansatz and…
The Gross-Pitaevskii equation - which describes interacting bosons in the mean-field approximation - possesses solitonic solutions in dimension one. For repulsively interacting particles, the stationary soliton is dark, i.e. is represented…
We study a two-component nonlinear Schr{\"{o}}dinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating…
Solitons are ubiquitous phenomena that appear, among others, in the description of tsunami waves, fiber-optic communication and ultracold atomic gases. The latter systems turned out to be an excellent playground for investigations of…
Schr\"odinger equation for Bose gas with repulsive contact interactions in one-dimensional space may be solved analytically with the help of the Bethe ansatz if we impose periodic boundary conditions. It was shown that in such a system…
The Lieb-Liniger model describes one-dimensional bosons with contact interactions. This many-body system admits an exact solution in terms of the Bethe ansatz. Some of the exact and perturbative results for this model are reviewed.…
A one-dimensional model of bosons with repulsive short-range interactions, solved analytically by Lieb and Liniger many years ago, predicts existence of two branches of elementary excitations. One of them represents Bogoliubov phonons, the…
The nonlinear coupling between the light beams and non-resonant ion density perturbations in a plasma is considered, taking into account the relativistic particle mass increase and the light beam ponderomotive force. A pair of equations…
The two-component Fermi gas with contact attractive interactions between different spin components can be described by the Yang-Gaudin model. Applying the Bethe ansatz approach, one finds analytical formulae for the system eigenstates that…
In the present contribution, we explore a host of different stationary states, namely dark-bright solitons and their lattices, that arise in the context of multi-component atomic Bose-Einstein condensates. The latter, are modeled by systems…
We consider the well-known Lieb-Liniger (LL) model for $N$ bosons interacting pairwise on the line via the $\delta$-potential in the mean-field scaling regime. Assuming suitable asymptotic factorization of the initial wave functions and…
Dark soliton solutions in the one-dimensional classical nonlinear Schr\"odinger equation has been considered to be related to the yrast states corresponding to the type-II excitations in the Lieb-Liniger model. However, the relation is…
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates (BECs). Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our…
Eigenstates of Bose particles with repulsive contact interactions in one-dimensional space with periodic boundary conditions can be found with the help of the Bethe ansatz. The type~II excitation spectrum identified by E. H. Lieb,…
Solitons are known to occur in the context of atom-light interaction via the well-known semi-classical phenomenon of self-induced transparency (SIT). Separately, in the regime where both light and atoms are fully treated quantum…
We reveal the existence of slowly-decaying dark solitons in the radiation build-up dynamics of bright pulses in all-normal dispersion mode-locked fiber lasers, numerically modeled in the framework of a generalized nonlinear Schr\"odinger…
Dark and grey soliton-like states are shown to emerge from numerically constructed superpositions of translationally-invariant eigenstates of the interacting Bose gas in a toroidal trap. The exact quantum many-body dynamics reveals a…
N-dark-dark solitons in the generally coupled integrable NLS equations are derived by the KP-hierarchy reduction method. These solitons exist when nonlinearities are all defocusing, or both focusing and defocusing nonlinearities are mixed.…
We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices. Using time-evolving block decimation to simulate the single-band Bose-Hubbard Hamiltonian, we consider…