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 …

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 …

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 …

This book provides a comprehensive treatment of the Gross–Pitaevskii equation with a
periodic potential; in particular, the localized modes supported by the periodic potential. It …

This article presents a concise survey of basic discrete and semi-discrete nonlinear models,
which produce two-and three-dimensional (2D and 3D) solitons, and a summary of the main …

We elaborate a fractional discrete nonlinear Schrödinger (FDNLS) equation based on an
appropriately modified definition of the Riesz fractional derivative, which is characterized by …

In the present work, we attempt a brief summary of various areas where non-linear waves
have been emerging in the phenomenology of lattice dynamical systems. These areas …

We study discrete vortices in the two-dimensional nonlinear Schrödinger lattice with small
coupling between lattice nodes. The discrete vortices in the anti-continuum limit of zero …

An array of linear resonators with alternating linear–nonlinear bonds can transition from a
topologically trivial to a nontrivial band structure as a function of the applied intensity. Here …

Non-Hermitian lattices with nonreciprocal couplings under open boundary conditions are
known to possess linear modes exponentially localized on one edge of the chain. This …