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.
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.