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内容説明 This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schr-dinger equation and the physical settings that it describes. It contains an introduction to the model， its systematic derivation and its connection to applications， a subsequent analysis of the existence and the stability of fundamental nonlinear structures in 1， 2 and even 3 spatial lattice dimensions. It also covers the case of defocusing nonlinearities， the modulational instabilities of plane wave solutions， and the extension to multi-component lattices. In addition， it features a final chapter on special topics written by a wide array of experts in the field， addressing through short reviews， areas of particular recent interest.