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 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 …

Solitons are among the most distinguishing fundamental excitations in a wide range of
nonlinear systems such as water in narrow channels, high-speed optical communication …

We report on the first experimental observation of bright matter wave solitons for Rb 87
atoms with repulsive atom-atom interaction. This counterintuitive situation arises inside a …

A negative effective mass can be realized in quantum systems by engineering the
dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently …

We report the first experimental observation of nonlinear self-trap** of Bose-condensed R
87 b atoms in a one-dimensional waveguide with a superimposed deep periodic potential …

We consider a problem of interference between two independent condensates that lack true
long-range order. We show that their interference pattern contains information about …

We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic
systems described by the nonlinear Schrödinger equation with a sinusoidal potential, such …

This review discusses progress in the new field of coherent matter waves, particularly with
respect to Bose–Einstein condensates. We give a short introduction to Bose–Einstein …

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 …