Topological photonics is an emerging field of research, which is inspired by the discovery of
topological insulators. The introduction of topology endows traditional photonic systems with …

We present a progress overview focused on the recent theoretical and experimental
advances in the area of soliton manipulation in optical lattices. Optical lattices offer the …

We show theoretically that a photonic topological insulator can support edge solitons that
are strongly self-localized and propagate unidirectionally along the lattice edge. The …

The question of whether features and behaviors that are characteristic to completely
integrable systems persist in the transition to non-integrable settings is a central one in the …

Using the method of asymptotics beyond all orders, we evaluate the amplitude of radiation
from a moving small-amplitude soliton in the discrete nonlinear Schrödinger equation. When …

The present work examines in detail the existence, stability and dynamics of travelling
solitary waves in a Schrödinger lattice with saturable nonlinearity. After analysing the linear …

Abstract While the Ablowitz-Ladik lattice is integrable, the Discrete Nonlinear Schrödinger
equation, which is more significant for physical applications, is not. We prove closeness of …

In this paper we analyze the existence, stability, dynamical formation, and mobility properties
of localized solutions in a one-dimensional system described by the discrete nonlinear …

We show that the state of amide-I excitations in proteins is modeled by the discrete nonlinear
Schrödinger equation with saturable nonlinearities. This is done by extending the Davydov …

We consider the question of existence of periodic solutions (called breather solutions or
discrete solitons) for the Discrete Nonlinear Schr\" odinger Equation with saturable and …