Ricardo Carretero-González - Nonlinear Dynamical Systems Group, Computational Science Research Center and Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720, United States (email)
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.
Published: December 2010.