Preface

Abstract

This issue of Discrete and Continuous Dynamical Systems - Series S is a compilation of papers representing the current state-of-the-art on the field of localized excitations and their role in the dynamics of complex physical systems. During the last two decades, an impressive volume of theoretical and experimental work has been devoted to the existence, stability and dynamics of such coherent structures. They have been identified as critical components of numerous continuous and discrete dynamical systems and, depending on the context (and their particular form), they may be referred to as solitons, instantons, kinks, breathers, or quodons, among many others. We nowadays think of such localized nonlinear excitations as being ubiquitous in nature due to their experimental realization in many diverse systems including, but not limited to, optical fibers and waveguide arrays, photonic crystals, Bose-Einstein condensates, molecular crystals, quasi-one-dimensional solids, Josephson-junctions and arrays thereof, layered silicates, micromechanical cantilever arrays, uranium crystals, pendulum arrays, water waves, electrical transmission lines, ferromagnetic and antiferromagnetic materials, granular crystals and so on. Additionally, they are also conjectured to play an important role in denaturation transitions and bubble formation in DNA, protein folding, atom ejection and defect migration in crystals, low-temperature reconstructive transformations, and many others. The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phenomena arising in nonlinear and complex systems, but also due to their potential for the development and "design" of novel applications. <br><br>For more information please click the “Full Text” above.