The Mathematical Theory of Permanent Progressive Water-wavesWorld Scientific, 2001 - 229 pages 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. |
Table des matières
Introduction | 1 |
Interfacial Progressive Waves | 8 |
Pure Capillary Waves | 31 |
Gravity Waves | 49 |
7 | 71 |
CapillaryGravity Waves | 83 |
67 | 101 |
Numerical Solutions of Mode 14 and 23 | 119 |
Waves of Negative Parameters | 137 |
Rotational Wave | 147 |
Solitary Waves | 197 |
217 | |
Autres éditions - Tout afficher
The Mathematical Theory of Permanent Progressive Water-waves Hisashi Okamoto,Mayumi Shōji Aucun aperçu disponible - 2001 |
Expressions et termes fréquents
analytic function assume axis represents bifurcation diagram bifurcation equation bifurcation theory bottom boundary condition branch of mode butterfly loop capillary waves capillary-gravity waves Chapter consider Crapper's waves crest curve define denotes diagram of capillary-gravity differential double bifurcation point existence finite fluid Fréchet derivative free boundary gravity waves highest wave Hilbert transform implies infinite depth Krasovskii Lemma Levi-Civita equation mathematical method neighborhood nontrivial solutions normal form Note O(2)-equivariance obtain parameter pitchfork bifurcation pitchfork of mode point of mode problem proof Proposition prove q-axis right hand side satisfies secondary bifurcation self-intersecting shows Sobolev space solitary waves solutions of mode stream function subcritical surface tension tên theorem transcritical bifurcation trivial solution turning points vanish water-waves wave profiles waves of mode Yamada zeros θσ მა მი მს მყ