MATHEMATICAL THEORY OF PERMANENT PROGRESSIVE WATER-WAVES, THE (Advanced Nonlinear Dynamics) - Hardcover

Okamoto, Hisashi; Shoji, Mayumi

Hardcover

ISBN 10: 9810244495 ISBN 13: 9789810244491

Publisher: World Scientific Publishing Company, 2001

Synopsis

This book is a self-contained introduction to the theory of periodic, progressive, permanent waves on the surface of incompressible inviscid fluid. The problem of permanent water-waves has attracted a large number of physicists and mathematicians since Stokes' pioneering papers appeared in 1847 and 1880. Among many aspects of the problem, the authors focus on periodic progressive waves, which mean waves traveling at a constant speed with no change of shape. As a consequence, everything about standing waves are excluded and solitary waves are studied only partly. However, even for this restricted problem, quite a number of papers and books, in physics and mathematics, have appeared and more will continue to appear, showing the richness of the subject. In fact, there remain many open questions to be answered.
The present book consists of two parts: numerical experiments and normal form analysis of the bifurcation equations. Prerequisite for reading it is an elementary knowledge of the Euler equations for incompressible inviscid fluid and of bifurcation theory. Readers are also expected to know functional analysis at an elementary level. Numerical experiments are reported so that any reader can re-examine the results with minimal labor: the methods used in this book are well-known and are described as clearly as possible. Thus, the reader with an elementary knowledge of numerical computation will have little difficulty in the re-examination.

About this title

Review

"...offers a self-contained introduction to the theory of periodic, progressive, permanent waves on the surface of incompressible inviscid fluid." -- Mathematics Abstracts, 2002

"The book should be of interest to scientists interested in the mathematical theory of water waves." -- Journal of Fluid Mechanics, 2003

Edition details

• Publisher: World Scientific Publishing Company
• Publication date: 2001
• ISBN 10: 9810244495
• ISBN 13: 9789810244491
• Binding: Hardcover
• Language: English
• Number of pages: 244