Related papers: Quasi-one-dimensional Bose-Einstein condensates in…
We explore the dynamical stabilities of a quasi-one dimensional (1D) Bose-Einstein condensate (BEC) consisting of fixed $N$ atoms with time-independent external potential. For the stationary states with zero flow density the general…
The existence and stability of solitons in Bose-Einstein condensates with attractive inter-atomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic…
Symbiotic solitons (SS) and quantum droplets (QD) are self-trapped localized modes emerging in binary Bose-gas mixtures with intra-component repulsion and inter-component attraction. We have shown that two-dimensional SS can be stabilized…
The dynamics of Bose-Einstein condensates in the lowest energy band of a one-dimensional optical lattice is generally disturbed by the presence of transversally excited resonant states. We propose an effective one-dimensional theory which…
The dynamics of localized excitations in array of Bose-Einstein condensates is investigated in the framework of the nonlinear lattice theory. The existence of temporarily stable ground states displaying an atomic population distributions…
We numerically study the dynamical excitations in Bose-Einstein condensate (BEC) placed in periodic and quasi-periodic 2D optical lattice (OL). In case of the repulsive mean-field interaction the BEC quantum tunnelling leads to a…
The intra-band tunneling of a Bose-Einstein condensate between three degenerate high-symmetry X-points of the Brillouin zone of a cubic optical lattice is studied in the quantum regime by reduction to a three-mode model. The mean-field…
The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schr\"odinger equation. If the…
We analyze the dynamical stability of gap solitons formed in a quasi one-dimensional Bose-Einstein condensate in an optical lattice. Using two different numerical methods we show that, under realistic assumptions for experimental…
We discuss localized ground states of Bose-Einstein condensates in optical lattices with attractive and repulsive three-body interactions in the framework of a quintic nonlinear Schr\"odinger equation which extends the Gross-Pitaevskii…
A Bose-Einstein condensate (BEC) confined in a one-dimensional lattice under the effect of an external homogeneous field is described by the Gross-Pitaevskii equation. Here we prove that such an equation can be reduced, in the semiclassical…
We present a thorough analysis of soliton solutions to the quasi-one-dimensional nonlinear Dirac equation (NLDE) for a Bose-Einstein condensate in a honeycomb lattice with armchair geometry. Our NLDE corresponds to a quasi-one-dimensional…
We derive an effective nonpolynomial Schrodinger equation (NPSE) for self-repulsive or attractive BEC in the nearly-1D cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. Besides the…
Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation we show that a bright soliton can be stabilized in a trapless three-dimensional attractive Bose-Einstein condensate (BEC) by a rapid periodic temporal…
Embedded solitons are rare self-localized nonlinear structures that, counterintuitively, survive inside a continuous background of resonant states. While this topic has been widely studied in nonlinear optics, it has received almost no…
The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a…
Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one, two, and three dimensional optical lattices. We find both stationary and nonstationary solutions,…
We propose a realistic experimental setup for creating quasi-two-dimensional (2D) bright solitons in dipolar Bose-Einstein condensates (BECs), the existence of which was proposed in Phys. Rev. Lett. 100, 090406 (2008). A challenging feature…
One-dimensional (1D) Nonlinear Schroedinger Equaation (NLS) provides a good approximation to attractive Bose-Einshtein condensate (BEC) in a quasi 1D cigar-shaped optical trap in certain regimes. 1D NLS is an integrable equation that can be…
Properties of localized states on array of BEC confined to a potential, representing superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice case the coupled mode system has been derived. The…