Synopses & Reviews
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.
Synopsis
Enables graduate students and researchers to understand and employ a wide variety of methods in applied mathematics.
Synopsis
This book describes the underlying approximation techniques and methods for finding solutions to nonlinear wave equations. Many chapters include exercise sets. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.
About the Author
Mark J. Ablowitz is Professor of Applied Mathematics at the University of Colorado, Boulder.
Table of Contents
Preface; Acknowledgements; Part I. Fundamentals and Basic Applications: 1. Introduction; 2. Linear and nonlinear wave equations; 3. Asymptotic analysis of wave equations; 4. Perturbation analysis; 5. Water waves and KdV type equations; 6. Nonlinear Schrödinger models and water waves; 7. Nonlinear Schrödinger models in nonlinear optics; Part II. Integrability and Solitons: 8. Solitons and integrable equations; 9. Inverse scattering transform for the KdV equation; Part III. Novel Applications of Nonlinear Waves: 10. Communications; 11. Mode-locked lasers; 12. Nonlinear photonic lattices; References; Index.