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

We review both theoretical and experimental advances in the recently emerged field of
modulated photonic lattices. These artificial periodic dielectric structures provide a powerful …

Solitons are localized wave disturbances that propagate without changing shape, a result of
a nonlinear interaction that compensates for wave packet dispersion. Individual solitons may …

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 …

In the course of the past several years, a new level of understanding has been achieved
about conditions for the existence, stability, and generation of spatiotemporal optical …

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 …

In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

In physics, wave propagation is traditionally analyzed by means of regular solutions of wave
equations. However, solutions of wave equations in two and three dimensions often possess …

In this review we try to capture some of the recent excitement induced by experimental
developments, but also by a large volume of theoretical and computational studies …

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 …