eBook - PDF

The Mathematical Theory of Permanent Progressive Water-Waves

Name: The Mathematical Theory of Permanent Progressive Water-Waves
Author: Hisashi Okamoto, Mayumi Sh??ji;;;

Hisashi Okamoto,

Mayumi Sh??ji;;;,

244 pages
English
PDF
Available on iOS & Android

eBook - PDF

The Mathematical Theory of Permanent Progressive Water-Waves

Hisashi Okamoto,

Mayumi Sh??ji;;;,

About this book

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.

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Yes, you can access The Mathematical Theory of Permanent Progressive Water-Waves by Hisashi Okamoto, Mayumi Sh??ji;;; in PDF and/or ePUB format, as well as other popular books in Physical Sciences & Applied Mathematics. We have over one million books available in our catalogue for you to explore.