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 …

Rapidly growing demands for fast information processing have launched a race for creating
compact and highly efficient optical devices that can reliably transmit signals without losses …

The Berry phase provides a modern formulation of electric polarization in crystals. We
extend this concept to higher electric multipole moments and determine the necessary …

Exploration of the impact of synthetic material landscapes featuring tunable geometrical
properties on physical processes is a research direction that is currently of great interest …

The topological protection of wave transport, originally observed in the context of the
quantum Hall effect in two-dimensional electron gases, has been shown to apply broadly to …

A nonlocal nonlinear Schrödinger (NLS) equation was recently found by the authors and
shown to be an integrable infinite dimensional Hamiltonian equation. Unlike the classical …

We present the first experimental observation of a topological transition in a non-Hermitian
system. In contrast to standard methods for examining topological properties, which involve …

Topological insulators are a new phase of matter, with the striking property that conduction
of electrons occurs only on their surfaces,,. In two dimensions, electrons on the surface of a …

We present the first experimental demonstration of a new type of localized state in the
continuum, namely, compacton-like linear states in flat-band lattices. To this end, we employ …