The field of nlinear dispersive waves has developed ermously since the work of Stokes, Boussinesq and Korteweg-de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nlinear wave equations, such as the KdV equation, governing a broad class of physical phemena that admit special solutions including those commonly kwn as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phemena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.
Mark J. Ablowitz is Professor of Applied Mathematics at the University of Colorado, Boulder.