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 …

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 phenomenon of Bose–Einstein condensation is a phase transition originally predicted
by Bose and Einstein in 1924. In particular, it was shown that below a critical temperature T …

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 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 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 …

In the present paper we use the Wannier function basis to construct lattice approximations of
the nonlinear Schrödinger equation with a periodic potential. We show that the nonlinear …

In this short topical review, we revisit a number of works on the pattern-forming dynamical
instabilities of Bose–Einstein condensates in one-and two-dimensional settings. In …

We demonstrate that a Bose-Einstein condensate in an optical lattice forms a reconfigurable
matter-wave structure with a band-gap spectrum, which resembles a nonlinear photonic …

We show that the phenomenon of modulational instability in arrays of Bose–Einstein
condensates confined to optical lattices gives rise to coherent spatial structures of localized …