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 …

In the course of the past several years, a new level of understanding has been achieved
about conditions for the existence, stability, and generation of spatiotemporal optical …

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 …

We present a progress overview focused on the recent theoretical and experimental
advances in the area of soliton manipulation in optical lattices. Optical lattices offer the …

We study various families of two-dimensional discrete or lattice solitons, and show that they
are possible only when their power level exceeds a critical threshold. In addition, we show …

The existence of stable solitons in two-and three-dimensional (2D and 3D) media governed
by the self-focusing cubic nonlinear Schrödinger equation with a periodic potential is …

Starting with a Gaussian variational ansatz, we predict anisotropic bright solitons in quasi-
2D Bose-Einstein condensates consisting of atoms with dipole moments polarized …

Using the variational approximation and direct simulations in real and imaginary time, we
find stable two-dimensional (2D) and 3D solitons in the self-attractive Gross-Pitaevskii …

We discuss localized ground states of Bose-Einstein condensates (BEC's) in optical lattices
with attractive and repulsive three-body interactions in the framework of a quintic nonlinear …