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We study the structure, stability, and dynamics of dark solitary waves in parabolically trapped, collisionally inhomogeneous Bose-Einstein condensates (BECs) with spatially periodic variations of the scattering length. This collisional…
We study a nonlinear Schroedinger equation arising in the mean-field description of dipolar quantum gases. Under the assumption of sufficiently strong dipolar interactions, the existence of standing waves, and hence solitons, is proved…
Axisymmetric three-dimensional solitary waves in uniform two-component mixture Bose-Einstein condensates are obtained as solutions of the coupled Gross-Pitaevskii equations with equal intracomponent but varying intercomponent interaction…
We study statically homogeneous Bose-Einstein condensates with spatially inhomogeneous interactions and outline an experimental realization of compensating linear and nonlinear potentials that can yield constant-density solutions. We…
We consider the dynamics of two coupled miscible Bose-Einstein condensates, when an obstacle is dragged through them. The existence of two different speeds of sound provides the possibility for three dynamical regimes: when both components…
We study Faraday and resonant waves in two-component quasi-one-dimensional (cigar-shaped) collisionally inhomogeneous Bose-Einstein condensates subject to periodic modulation of the radial confinement. We show by means of extensive…
We unveil the dynamical formation of multiple localized structures in the form of dark-bright and dark-antidark solitary waves that emerge upon quenching a one-dimensional particle-imbalanced Bose-Bose mixture. Interspecies interaction…
We theoretically investigate the out-of-equilibrium dynamics in a binary Bose-Einstein condensate confined within two-dimensional box potentials. One species of the condensate interacts with a pair of oppositely wound, but otherwise…
We investigate the localized nonlinear matter waves of the quasi-two dimensional Bose-Einstein condensates with spatially modulated nonlinearity in harmonic potential. It is shown that the whole Bose-Einstein condensates, similar to the…
We investigate parametric excitation and pattern formation in a harmonically trapped two-component Bose-Einstein condensate. We assume the condensate to be in the miscible phase, but near the miscible-immiscible phase transition, where…
X-waves are an example of a localized wave packet solution of the homogeneous wave equation, and can potentially arise in any area of physics relating to wave phenomena, such as acoustics, electromagnetism, or quantum mechanics. They have…
We consider dynamics of simple waves in a two-component Bose-Einstein condensates. The evolution of the condensate is described by the Gross-Pitaevskii equations which can be reduced for simple wave solutions to a system of ordinary…
A key feature of ultra-light dark matter composed by bosons is the formation of superfluid Bose-Einstein condensate (BEC) structures on galactic scales. We study collisions of BEC solitonic and vortex structures in the framework of the…
We numerically study the dynamics of vortex lattice formation in a rotating cigar-shaped Bose-Einstein condensate. The study is a three-dimensional simulation of the Gross-Pitaevskii equation with a phenomenological dissipation term. The…
We report on the controlled creation of multiple soliton complexes of the dark-bright type in one-dimensional two-component, three-component and spinor Bose-Einstein condensates. The formation of these states is based on the so-called…
We model the dynamics of formation of multiple, long-lived, bright solitary waves in the collapse of Bose-Einstein condensates with attractive interactions as studied in the experiment of Cornish et al. [Phys. Rev. Lett. 96 (2006) 170401].…
Quasi-one-dimensional solitons that may occur in an elongated Bose-Einstein condensate become unstable at high particle density. We study two basic modes of instability and the corresponding bifurcations to genuinely three-dimensional…
Vortex lattices in rapidly rotating Bose-Einstein condensates lead to a periodic modulation of the superfluid density with a triangular symmetry. Here we show that this symmetry can be combined with an external perturbation in order to…
We construct rogue wave and breather solutions of a quasi-two-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap. We show that the trapping potential and an arbitrary functional parameter…
We propose a method for generating shock waves in Bose-Einstein condensates by rapidly increasing the value of the nonlinear coefficient using Feshbach resonances. We show that in a cigar-shaped condensate there exist primary (transverse)…