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 …

In this review we try to capture some of the recent excitement induced by experimental
developments, but also by a large volume of theoretical and computational studies …

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 …

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 …

An experimentally realizable scheme of periodic sign-changing modulation of the scattering
length is proposed for Bose-Einstein condensates similar to dispersion-management …

In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE)
on a finite but large spatial domain x∈[0, L], x= x (x, y, z) and t∈[0, T] are considered. Also in …

We investigate the localized nonlinear matter waves of the quasi-two-dimensional Bose-
Einstein condensates with spatially modulated nonlinearity in the harmonic potential. It is …

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 …

The nonlinear Schrödinger equation is a very versatile equation used in many branches of
physics, dictating the behavior of wave packets in weakly nonlinear media. From the …

Abstract When two Bose–Einstein condensates collide with high collisional energy, the
celebrated matter-wave interference pattern appears. For lower collisional energies, the …