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Mathematical Theory Of Permanent Progressive Water-waves, The (Paperback)
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Mathematical Theory Of Permanent Progressive Water-waves, The (Paperback)
Series: Advanced Series in Nonlinear Dynamics, 20
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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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