Nonlinear Water Waves

This volume
brings together four lecture courses on modern aspects of water waves. The
intention, through the lectures, is to present quite a range of mathematical
ideas, primarily to show what is possible and what, currently, is of particular
interest.

Water waves
of large amplitude can only be fully understood in terms of nonlinear effects,
linear theory being not adequate for their description. Taking advantage of
insights from physical observation, experimental evidence and numerical
simulations, classical and modern mathematical approaches can be used to gain
insight into their dynamics. The book presents several avenues and offers a
wide range of material of current interest. Due to the interdisciplinary nature
of the subject, the book should be of interest to mathematicians (pure and
applied), physicists and engineers.

The
lectures provide a useful source for those who want to begin to investigate how
mathematics can be used to improve our understanding of water wave phenomena.
In addition, some of the material can be used by those who are already familiar
with one branch of the study of water waves, to learn more about other areas.
The lectures cover background material as well as aspects that represent the
state-of-the-art. We therefore commend this collection of lectures to both the
novice and the expert.