Nonlinear Dispersive Waves Asymptotic Analysis and Solitons
Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons by Mark J. Ablowitz, published by Cambridge University Press on September 8, 2011, is a comprehensive exploration of the field of nonlinear dispersive waves. Spanning 362 pages, this book delves into the evolution of the subject since the foundational work of Stokes, Boussinesq, and Korteweg-de Vries in the nineteenth century, highlighting the development of asymptotic methods for deriving nonlinear wave equations. It presents a detailed overview of approximation techniques and methods for solving these equations, including the well-known KdV equation.
Readers will find a thorough examination of concepts such as wave dispersion, asymptotic analysis, and perturbation theory, along with applications in areas like nonlinear optics and wave phenomena. The book includes exercise sets in most chapters, making it suitable for advanced courses and self-directed learning. Graduate students and researchers will benefit from the insights provided, as the text bridges the disciplines of applied mathematics, engineering, and physical science, offering a solid foundation in this dynamic field.
Official synopsis Publisher
The field of nonlinear dispersive waves has developed enormously 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 nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known 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, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. 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.
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