A Modern Introduction to the Mathematical Theory of Water Waves

by R. S. Johnson

Overview

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.

Product Details

ISBN-13:	9780521591720
Publisher:	Cambridge University Press
Publication date:	10/28/1997
Series:	Cambridge Texts in Applied Mathematics , #19
Pages:	464
Product dimensions:	6.26(w) x 9.33(h) x 1.22(d)

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.

Editorial Reviews

"...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

From the Publisher