Nonlinear Waves in Integrable and Non-integrable Systems presents cutting-edge developments in the theory and experimental study of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for non-integrable systems is the first of its kind. The book also discusses in great depth a wide range of analytical methods for integrable equations and comprehensively describes efficient numerical methods for all major aspects of nonlinear wave computations. It contains a chapter on nonlinear waves in periodic media, where many novel phenomena due to bandgap guidance are revealed and thoroughly analyzed. It presents the latest experiments on nonlinear waves in optical systems and Bose-Einstein condensates, especially in periodic media. The book also contains a large number of simple and efficient MATLAB codes for various types of nonlinear wave computations, which readers can easily adapt to solve their own problems.