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 …

Extended shallow water wave equations are derived, using the method of asymptotic
expansions, from the Euler (or water wave) equations. These extended models are valid one …

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 present a systematic study on the dynamics of a ultraslow optical soliton in a cold, highly
resonant three-state atomic system under Raman excitation. Using a method of multiple …

The head-on collision of ion acoustic solitary waves in a three-component unmagnetized
plasma with cold ions, Boltzmann distributed positrons, and superthermal electrons is …

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 …

The reductive perturbation method is a very powerful way of deriving simplified models
describing nonlinear wave propagation and interaction. In abstract frames chosen for the …

For partial differential equations (PDEs) that have n≥ 2 independent variables and a
symmetry algebra of dimension at least n− 1, an explicit algorithmic method is presented for …

We present measurements of the critical velocity for vortex shedding in a highly oblate Bose-
Einstein condensate with a moving repulsive Gaussian laser beam. As a function of the …