Synopses & Reviews
For over a hundred years, the theory of water waves has been a source of intriguing and often difficult mathematical problems. Virtually every classical mathematical technique appears somewhere within its confines. Beginning with the introduction of the appropriate equations of fluid mechanics, the opening chapters of this text consider the classical problems in linear and nonlinear water-wave theory. This sets the stage for a study of more modern aspects, problems that give rise to soliton-type equations. The book closes with an introduction to the effects of viscosity. All the mathematical developments are presented in the most straightforward manner, with worked examples and simple cases carefully explained. Exercises, further reading, and historical notes on some of the important characters in the field round off the book and make this an ideal text for a beginning graduate course on water waves.
Review
"...reasonably priced, and it is one of the best books available on the subject. With suitable supplements by the instructor, it could serve as a very readable text for an interesting course on the modern theory of water waves." Mathematical Reviews
Review
"...reasonably priced, and it is one of the best books available on the subject. With suitable supplements by the instructor, it could serve as a very readable text for an interesting course on the modern theory of water waves." Mathematical Reviews
Synopsis
This text considers classical and modern problems in linear and non-linear water-wave theory.
Synopsis
The theory of water waves has been a source of intriguing and oftendifficult mathematical problems for at least 150 years. This text briefly discusses fluid mechanics. It then considers the classical problems in linear and non-linear water-wave theory, as well as more modern aspects -- problems that give rise to soliton-type equations. Lastly it examines the effects of viscosity. All the mathematical developments are presented in a straightforward manner. Exercises, further reading, and historical notes make this an ideal text for graduate students.
Table of Contents
1. Mathematical preliminaries; 2. Some classical problems in water-wave theory; 3. Weakly nonlinear dispersive waves; 4. Slow modulation of dispersive waves; 5. Epilogue.