PREFACE

Localized excitations have been at the heart of developments of nonlinear dynamics (and especially of nonlinear complex systems) during the past few decades. Their names may vary (solitons, instantons, kinks, breathers, vortices, vortex rings, quodons, etc.), yet their relevance is ubiquitous and their importance undisputed not only in a wide variety of mathematical and theoretical developments but also in a broad range of applications. The latter constitute an ever-expanding list including, but certainly not limited to, Bose-Einstein condensates in atomic physics, optical fibers, waveguide arrays and photorefractive systems in nonlinear optics, Josephson junctions and arrays thereof, molecular crystals, layered silicates, ferromagnetic and antiferromagnetic materials, granular crystals, micromechanical cantilever or simple torsion pendulum arrays, electrical transmission lines, and nematic liquid crystals. Additionally, in many other cutting edge areas, they have been conjectured to not only emerge but also play a critical role in the dynamics and the explanation of experimental observations. Such fields include graphene nanoribbons, denaturation of the DNA double strand, atomic ejection and defect migration in crystals, and protein folding. It is thus clear that this is a subject which is fundamental for both theory and applications, and the evaluation of its state-of-the-art and the identification of the challenges that lie ahead are of paramount importance. Clearly, nonlinear science matures and continues to redefine itself, playing an increasingly important and ever-expanding role within the twenty-first century. The 2nd Conference on “Localized Excitations in Nonlinear Complex Systems” (LENCOS’12) was organized with the aim of bringing together experimental and theoretical physicists, chemists, biologists, and applied mathematicians working in the broad field of nonlinear localized modes. This workshop was the second installment in the series, following up on the successful first conference that took place 3 years earlier (LENCOS’09). The latter meeting provided the opportunity for a special volume on the themes of the workshop which appeared in the journal Discrete and Continuous Dynamical Systems – Series S (DCDS-S). Despite its short history, LENCOS has garnered considerable visibility and is already a widely appreciated venue for interdisciplinary exchanges and the promotion of research in this multifaceted and diverse thematic area. Both installments were