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 …

We predict the existence of rogue waves in Bose-Einstein condensates either loaded into a
parabolic trap or embedded in an optical lattice. In the latter case, rogue waves can be …

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 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 …

One-dimensional topological pumping of matter waves in two overlaid optical lattices
moving with respect to each other is considered in the presence of attractive nonlinearity. It …

Stochastically driven nonlinear processes are responsible for spontaneous pattern formation
and instabilities in numerous natural and artificial systems, including well-known examples …

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 …

It is known that rogue waves (RWs) are generated by the modulational instability (MI) of the
baseband type. Starting with the Bers-Kaup-Reiman system for three-wave resonant …