DNLS with Impurities

Abstract

The past few years have witnessed an explosion of interest in discrete models and intrinsic localized modes (discrete breathers or solitons) that has been summarized in a number of recent reviews [1–3]. This growth has been motivated by numerous applications of nonlinear dynamical lattice models in areas as broad and diverse as the nonlinear optics of waveguide arrays [4], the dynamics of Bose–Einstein condensates in periodic potentials [5, 6], micro-mechanical models of cantilever arrays [7], or even simple models of the complex dynamics of the DNA double strand [8]. Arguably, the most prototypical model among the ones that emerge in these settings is the Discrete Nonlinear Schrödinger (DNLS) equation, the main topic of this book.