Matter waves inside periodic potentials are well known from solid-state physics, where
electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates …

We provide an overview of recent experimental and theoretical developments in the area of
optical discrete solitons. By nature, discrete solitons represent self-trapped wavepackets in …

This review paper presents an overview of the theoretical and experimental progress on the
study of matter-wave dark solitons in atomic Bose–Einstein condensates. Upon introducing …

The aim of this introductory article is two-fold. First, we aim to offer a general introduction to
the theme of Bose-Einstein condensates, and briefly discuss the evolution of a number of …

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 …

The aim of this review is to introduce the reader to some of the physical notions and the
mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein …

A self-consistent theory of a cylindrically shaped Bose-Einstein condensate (BEC)
periodically modulated by a laser beam is presented. We show, both analytically and …

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 …

We analyze the existence and stability of spatially extended (Bloch-type) and localized
states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the …

It is unanimously accepted that the quantum and the classical descriptions of the physical
reality are very different, although any quantum process is" mysteriously" transformed …