This paper reviews the recent theoretical and experimental advances in the study of ultra-
cold gases made of bosonic particles interacting via the long-range, anisotropic dipole …

A survey of some recent theoretical and experimental studies on localized structures that
form and propagate in a broad class of optical and matter-wave media is presented. The …

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 …

Spatiotemporal mode coupling in highly multimode physical systems permits new routes for
exploring complex instabilities and forming coherent wave structures. We present here the …

The dynamics of wave packets in the fractional Schrödinger equation is still an open
problem. The difficulty stems from the fact that the fractional Laplacian derivative is …

We study the behavior of a Bose-Einstein condensate in which atoms are weakly coupled to
a highly excited Rydberg state. Since the latter have very strong van der Waals interactions …

We present a family of exact solutions of the one-dimensional nonlinear Schrödinger
equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with …

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 report numerical evidence of Hawking emission of Bogoliubov phonons from a sonic
horizon in a flowing one-dimensional atomic Bose–Einstein condensate. The presence of …

Using similarity transformations we construct explicit nontrivial solutions of nonlinear
Schrödinger equations with potentials and nonlinearities depending both on time and on the …