Author: F Palmero   (pdf slides, 2.4 Mb).
With J. Cuevas. L. English, R. Carretero and P. Kevrikidis

Abstract: Nonlinear physics of discrete systems has witnessed enormous development in the past years. In particular, a great deal of attention has been paid to the existence and properties of intrinsic localized modes, or discrete breathers, which result from the combination of nonlinearity and spatial discreteness. Their existence and  persistence under general conditions has been proved mathematically, observed in a wide variety of different systems, and recently, in some cases, the direct control and manipulation of such states has been enabled experimentally.

We will review some contributions in the field of discrete breathers, and focus on a particular set of systems, a family of closely related macroscopic electrical lattices, where dynamics can be measured fully in space and time, and also characterized theoretically by means of simple models. These systems are, arguably, ideal to make quantitative contact between theoretical and experimental results. Also, we have achieved a substantial spatial control of these excitations.

Dickinson College, Pennsylvania, USA, August 30, 2012.