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 …

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 …

Recent experimental and theoretical advances in the creation and description of bright
matter wave solitons are reviewed. Several aspects are taken into account, including the …

A new route to coherent destruction of tunneling is established by considering a
monochromatic fast modulation of the self-interaction strength of a many-boson system. The …

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 analyze the response of rational and regular (hyperbolic-secant) soliton solutions of an
extended nonlinear Schrödinger equation (NLSE) which includes an additional self …

Optical rogue waves of the coupled nonlinear Schrödinger equations with negative coherent
coupling, which describe the propagation of orthogonally polarized optical waves in an …

We study the motion of bright matter-wave solitons in nonlinear potentials, produced by
periodic or random spatial variations of the atomic scattering length. We obtain analytical …

The dynamics of a two-dimensional Bose-Einstein condensate in a presence of quantum
fluctuations is studied. The properties of localized density distributions, quantum droplets …

We examine the parametric and modulational instabilities arising in a non-autonomous,
discrete nonlinear Schrödinger equation. The principal motivation for our study stems from …