Recent progress on nonlinear properties of parity-time (PT)-symmetric systems is
comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum …

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 …

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 …

The stability of nonlinear waves has a distinguished history and an abundance of richly
structured yet accessible examples, which makes it not only an important subject but also an …

Originally, the Hubbard model was derived for describing the behavior of strongly correlated
electrons in solids. However, for over a decade now, variations of it have also routinely been …

This review paper presents an overview of the theoretical and experimental progress on the
study of matter-wave dark solitons in atomic Bose–Einstein condensates. Upon introducing …

A salient feature of solid-state quantum-Hall-type topological materials in two dimensions is
the presence of conducting electronic edge states that are insensitive to scattering by …

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 many contexts, interaction between particles gives rise to emergent phenomena. An
example is the fractional quantum Hall effect, where the interaction between electrons leads …

Exploring the interplay between topological band structures and tunable nonlinearities has
become possible with the development of synthetic lattice systems. In this emerging field of …