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 …

Nonlinear classical Hamiltonian lattices exhibit generic solutions—discrete breathers. They
are time-periodic and (typically exponentially) localized in space. The lattices have discrete …

Over the last few years arrays of evanescently coupled waveguides have been brought into
focus as a particular representation of functionalized optical materials, in which the …

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

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 present a versatile scheme for creating topological Bogoliubov excitations in weakly
interacting bosonic systems. Our proposal relies on a background stationary field that …

The observation of a two-dimensional discrete soliton in a cubic 5× 5 fs laser written
waveguide array in fused silica is reported for the first time. In addition to the localization the …

The observation of discrete spatial solitons in fs laser written waveguide arrays in fused
silica is reported for the. rst time. The fs writing process permits the speci. c setting of the …

We introduce a dynamical model of a Bose-Einstein condensate based on the one-
dimensional (1D) Gross-Pitaevskii equation (GPE) with a nonlinear optical lattice (NOL) …

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 …