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Self-trapping is a hallmark phenomenon of nonlinear dynamics. It has significant applications in modern physics, including band structure engineering, phase transition dynamics, quantum metrology, and more. Dilute-gas Bose-Einstein…
A binary mixture of interacting Bose-Einstein condensates (BEC) in the presence of fragmentation-driving external lattice potentials forms two interdependent mean-field lattices made of each component. These effective mean-field lattices,…
We have experimentally studied the unstable dynamics of a harmonically trapped Bose-Einstein condensate loaded into a 1D moving optical lattice. The lifetime of the condensate in such a potential exhibits a dramatic dependence on the…
We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero…
The dynamics of static and travelling breathers in two-species Bose-Einstein condensates in a one-dimensional optical lattice is modelled within the tight-binding approximation. Two coupled discrete nonlinear Schr\"odinger equations…
By numerical simulation of the time-dependent Gross-Pitaevskii equation we show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC) vortex can be localized in a three-dimensional bichromatic quasi-periodic…
This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history. Some findings, such as optical solitons supported by thermal nonlinearity, and by the orientational nonlinearity…
We theoretically investigate the dynamics of modulation instability (MI) in two-dimensional spin-orbit coupled Bose-Einstein condensates (BECs). The analysis is performed for equal densities of pseudo-spin components. Different combination…
The hydrodynamic equations of superfluids for a weakly interacting Bose gas are generalized to include the effects of periodic optical potentials produced by stationary laser beams. The new equations are characterized by a renormalized…
We use the time-dependent mean-field Gross-Pitaevskii equation to study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose-Einstein condensate (BEC). Because of three-body…
In the present paper, we investigate the dynamics of a Bose-Einstein condensates (BEC) loaded into an deep optical lattice of 1D, 2D and 3D, both analytically and numerically. We focus on the self-trapping state and the effect of the system…
By numerical and variational solution of the Gross-Pitaevskii equation, we studied the localization of a noninteracting and weakly-interacting Bose-Einstein condensate (BEC) in a disordered cold atom lattice and a speckle potential. In the…
We investigate localization transitions in interacting Bose-Einstein condensates (BECs) confined in tilted optical lattices, focusing on both the continuum limit accessed via shallow lattice depths and the tight-binding limit realized in…
A strongly dipolar Bose-Einstein condensate (BEC) of Dy atoms could sustain different types of states not possible in a non-dipolar BEC. Motivated by the observation of a very strongly dipolar condensate of NaCs molecules [N. Bigagli et…
In this paper we study the soliton dynamics of a high-density Bose-Einstein condensate (BEC) subject to a time-oscillating trap. The behavior of the BEC is described with a modified Gross-Pitaevskii equation (mGPE) which takes into account…
It was recently proved that isolated unstable "embedded lattice solitons" (ELS) may exist in discrete systems. The discovery of these ELS gives rise to relevant questions such as the following: are there continuous families of ELS?, can ELS…
Dynamics of atomic and molecular bright solitons in a hybrid atom-molecular BEC (Bose Einstein Condensate) system of 85Rb coupled through Magnetic Feshbach Resonance (MFR) has been investigated. By solving the time independent…
We experimentally study the effect of inter-particle interactions on the flat-band states of a two-dimensional Lieb lattice with drive and dissipation. Exploiting the giant nonlinear interactions of exciton polaritons we observe compactly…
We demonstrate robust, stable, mobile excited states of quasi-two-dimensional (quasi-2D) dipolar Bose-Einstein condensate (BEC) solitons for repulsive contact interaction with a harmonic trap along the $x$ direction perpendicular to the…
We describe wave propagation and soliton localization in photonic lattices which are induced in a nonlinear medium by an optical interference pattern, taking into account the inherent lattice deformations at the soliton location. We obtain…