The purpose of this book is to present a self contained introduction to the mathematical and physical aspects of the theory of water waves. The book is aimed at undergraduate and graduate levels for engineers, physical scientists and mathematicians. Each chapter is concluded with practical problems expressed as exercises and accompanied by ample references for further studies. The book consists of ten chapters arranged into three parts: Part I: Basic Fluid Mechanics and Solutions Techniques which cover chapters 1-3. Part II: Water Waves covering chapters 4-7. Part III Advanced Water Waves which covers chapters 8-10. Parts I and II are elementary in nature; whereas Part III is more advanced.
The first three chapters give the derivations of the fundamental mathematical equations. Chapter 2 outlines appropriate differential equations to describe the physical phenomena, and Chapter 3 reviews solution techniques of some simplified partial differential equations. Chapter 4 gives the developmental of wave equations, including the essential boundary conditons and describes small amplitude wave theory. Chapter 5 deals with finite amplitude wave theory and Chapter 6 outlines the study of tidal dynamics in shallow water. For random wave case, the deterministic methods described in previous chapters do not hold good. Therefore, chapter 7 is clearly devoted to wave statistics and wave energy spectrum. The application of wave theory is demonstrated in Chapter 8. Chapter 9 examines the nonlinear long waves in shallow water from a mathematical view point. The book concludes with Chapter 10 which illustrates the inverse scattering technique to solve solitary wave problem.
Matiur Rahman is at Technical University of Nova Scotia.
'This book is well written and can be easily read. It is self-contained in that all of the mathematical tools and equations the reader needs can be found in the book. It is of interest to a wide audience in the science community: mathematicians, physicists, and engineers. Any reader would have to refer to numerous other book s to get all the information found here...
I recommend this book to anyone who wishes to learn more about water waves and who has some fluid mechanics and applied mathematics background. It is a valuable book to have in one's library if one is interested in wave phenomena...' Anne C. Morlet, SIAM Review, Vol. 39 No. 1, March 1997