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 …

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 …

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 …

We consider vector solitons of mixed bright-dark types in quasi-one-dimensional spinor (F=
1) Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the …

We investigate the dynamics of matter-wave solitons in the presence of a spatially varying
atomic scattering length and nonlinearity. The dynamics of bright and dark solitary waves is …

In this brief review we summarize a number of recent developments in the study of vortices
in Bose–Einstein condensates, a topic of considerable theoretical and experimental interest …

The interaction of matter–wave solitons with a potential barrier is a fundamentally important
problem, and the splitting and subsequent recombination of the soliton by the barrier is the …

We theoretically investigate the scattering of bright solitons in a Bose-Einstein condensate
on narrow attractive potential wells. Reflection, transmission, and trapping of an incident …

By taking the plane wave potentials as the seed solutions, we harness a binary Darboux
transformation to generate dark vector soliton solutions for multi-component nonlinear …