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 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 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 …

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-
wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of …

Using Lie group theory and canonical transformations, we construct explicit solutions of
nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities. We present …

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

Dispersive shock waves are fascinating phenomena occurring when nonlinearity
overwhelms linear effects, such as dispersion and diffraction. Many features of shock waves …

We explore, both experimentally and theoretically, the response of an elongated Bose-
Einstein condensate to modulated interactions. We identify two distinct regimes differing in …

We investigate the formation of collisionless shocks along the spatial profile of a Gaussian
laser beam propagating in nonlocal nonlinear media. For defocusing nonlinearity the shock …

We investigate the propagation of a dark beam in a defocusing medium in the strong
nonlinear regime. We observe for the first time a shock fan filled with noninteracting one …