Abstract 2D and 3D solitons and related states, such as quantum droplets, can appear in
optical systems, atomic Bose–Einstein condensates (BECs) and liquid crystals, among other …

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 …

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 …

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 …

This article offers a review of (chiefly, theoretical) results for self-trapped states (solitons) in
two-and three-dimensional (2D and 3D) models of nonlinear dissipative media. The …

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 …

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 …

We consider several effects of the matter wave dynamics which can be observed in Bose–
Einstein condensates embedded into optical lattices. For low-density condensates, we …

We report on the first experimental observation of discrete vortex solitons in two-dimensional
optically induced photonic lattices. We demonstrate strong stabilization of an optical vortex …

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 …