We present an overview of nonlinear phenomena related to optical quadratic solitons—
intrinsically multi-component localized states of light, which can exist in media without …

In this paper we review a number of recent developments in the study of the Discrete
Nonlinear Schrödinger (DNLS) equation. Results concerning ground and excited states …

From protein motifs to black holes, topological solitons are pervasive nonlinear excitations
that are robust and can be driven by external fields. So far, existing driving mechanisms all …

The current research into solitons and their use in fiber optic communications is very
important to the future of communications. Since the advent of computer networking and …

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 …

Theoretical physics deals with physical models. The main requirements for a good physical
model are simplicity and universality. Universal models which can be applied to describe a …

We predict a dynamical classical superfluid-insulator transition in a Bose-Einstein
condensate trapped in an optical and a magnetic potential. In the tight-binding limit, this …

We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic
systems described by the nonlinear Schrödinger equation with a sinusoidal potential, such …

We prove for a class of nonlinear Schrödinger systems (NLS) having two nonlinear bound
states that the (generic) large time behavior is characterized by decay of the excited state …

The Discrete Nonlinear Schrödinger (DNLS) equation describes a particularly simple model
for a lattice of coupled anharmonic oscillators. In one spatial dimension, the equation in its …