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 …

Parity-time (PT) symmetry is nowadays an active area of research, having an impact in both
science and technology. Parity-time concepts first originated within the framework of …

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 study the families of nonlinear modes described by the nonlinear Schrödinger equation
with the PT-symmetric harmonic potential x 2− 2 i α x. The nonlinear modes found display a …

We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-
Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark …

Hyperspherical harmonics are extremely useful in nuclear physics and reactive scattering
theory. However, their use has been confined to specialists with very strong backgrounds in …

We theoretically consider effectively one-dimensional quantum droplets in a symmetric Bose-
Bose mixture confined in a parabolic trap. We systematically investigate ground and excited …

Abstract The energies of Bose–Einstein condensate of 85 Rb atoms confined by the 3-
dimensional parabolic and quartic trap are investigated. The two-body correlations among …

Abstract Excited states of Bose–Einstein condensates are considered in the large density
limit of the Gross–Pitaevskii equation with repulsive inter-atomic interactions and a harmonic …

We consider spatial solitons as, for example, self-confined optical beams in spaces of
constant curvature, which are a natural generalization of flat space. Due to the symmetries of …