Since the realization of Bose–Einstein condensates (BECs) trapped in optical potentials,
intensive experimental and theoretical investigations have been carried out for bright and …

This article offers a comprehensive survey of results obtained for solitons and complex
nonlinear wave patterns supported by nonlinear lattices (NLs), which represent a spatially …

Quantum fluctuations can stabilize Bose–Einstein condensates (BEC) against the mean-
field collapse. Stabilization of the condensate has been observed in quantum degenerate …

A comparative review is given of some well-known and some recent results obtained in
studies of two-and three-dimensional (2D and 3D) solitons, with emphasis on states carrying …

Novel soliton solutions for the nonautonomous nonlinear Schrödinger equation models with
linear and harmonic oscillator potentials substantially extend the concept of classical …

Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional
equations are well known in anomalous diffusion. We connect these two fields by presenting …

The aim of this introductory article is two-fold. First, we aim to offer a general introduction to
the theme of Bose-Einstein condensates, and briefly discuss the evolution of a number of …

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 …

It was recently found that the Lee-Huang-Yang (LHY) correction to the mean-field
Hamiltonian of binary atomic boson condensates suppresses the collapse and creates …

We present the first realization of a solitonic atom interferometer. A Bose-Einstein
condensate of 1× 10 4 atoms of rubidium-85 is loaded into a horizontal optical waveguide …