We consider several effects of the matter wave dynamics which can be observed in Bose–
Einstein condensates embedded into optical lattices. For low-density condensates, we …

In this brief review we summarize a number of recent developments in the study of vortices
in Bose–Einstein condensates, a topic of considerable theoretical and experimental interest …

We discuss the propagation and interaction of discrete quantum droplets in one-dimensional
binary Bose mixtures by variationally and numerically solving the underlying generalized …

We analyze the existence and stability of localized solutions in the one-dimensional discrete
nonlinear Schrödinger (DNLS) equation with a combination of competing self-focusing cubic …

We introduce one-and two-dimensional (1D and 2D) continuum and discrete models for the
two-component BEC, with the spin-orbit (SO) coupling of the Rashba type between the …

We study the existence, stability, and mobility of fundamental discrete solitons in two-and
three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing …

A model of the Bose-Einstein condensate of dipolar atoms, confined in a combination of a
cigar-shaped trap and deep optical lattice acting in the axial direction, is introduced, taking …

In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear
Schrödinger equation, we find discrete vortex solitons with various values of the topological …

We show for the first time that supratransmission threshold can be found in discrete
nonlinear Schrödinger equation modelling the optical waveguide arrays with Kerr …

We propose a possible way to excite breathers on the one-dimensional quantum droplets,
which benefit from the introduction of quantum fluctuation and locally exhibit the …