A Modern Introduction to the Mathematical Theory of Water Waves


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.


 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

' … the book would amke an excellent textbook for graduate or advanced undergraduate courses'. J. D. Gibbon, UK Nonlinear Science News

'This is an excellent textbook suitable to the last-year undergraduate students in applied mathematics, physics, or engineering, as well as to the first-year graduate students in similar areas.' Zietschrift fur Angwandte Mathematik und Physik

'The book is a valuable source of information on the mathematic theory of water gravity waves and I am very pleased to have it on my shelf. I would recommend it to anyone who deals or is going to deal with this subject, but first for all to mathematically inclined readers.' M. Markiewicz, ZAMM

' … the publication of this book will be welcomed by researchers and postgraduate students in water-wave theory.' C. M. Linton, Contemporary Physics

'This is a well-written book that is a pleasure to read.' T. R. Akylas, European Journal of Mechanics