Nonlinear Dispersive Waves
Nonlinear Dispersive Waves
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.
- Covers a wide variety of methods
- Ideal for graduate courses in nonlinear waves
- Classroom tested by the author
Reviews & endorsements
"It is an up-to-date teaching resource that will prepare students for work in nonlinear waves as the subject appears today in applications, especially in nonlinear optics. It is clear that Mark Ablowitz's book is a welcome addition to the literature that will be particularly useful to anyone planning a course on nonlinear waves."
Peter D. Miller, SIAM News
"This text is a guide, suitable for advanced undergraduate or beginning graduate students but also useful for more mature analysts with a passing familiarity with the field, to some basic techniques for modelling nonlinear waves with partial differential equations."
John Albert, Mathematical Reviews
Product details
October 2011Paperback
9781107664104
362 pages
229 × 151 × 19 mm
0.52kg
65 b/w illus. 85 exercises
Available
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.
