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 waterwaves, to learn more about other areas.

Equally interesting for mathematicians (pure and applied), physicists and engineers due to the interdisciplinary nature of the subject Covers background material as well as aspects that represent the state-of-the-art therefore recommended both for the novice and the expert The discussions cover a wide range of open

Autorentext

Adrian Constantin ist Professor für Mathematik an der Universität Wien. Er diplomierte 1992 an der Universität Nizza, promovierte 1996 an der New York University und habilitierte sich 1999 an der Universität Zürich. Er war Mathematik-Lehrstuhlinhaber an der Universität Lund (2000-2008 ), am Trinity College Dublin (2004-2008), am King's College London (2012-2014) und seit 2008 ist er Universitätsprofessor für Partielle Differentialgleichungen an der Universität Wien. 2022 wurde er in die deutsche Nationale Akademie der Wissenschaften Leopoldina aufgenommen, und seit 2022 ist er auch korrespondierendes Mitglied der Österreichischen Akademie der Wissenschaften.

Inhalt
Adrian Constantin: Exact travelling periodic water waves in two-dimensional irrotational flows.- Joachim Escher: Breaking Water Waves.- Robin Stanley Johnson: Asymptotic methods for weakly nonlinear and other water waves.- Gabriele Villari: A survival kit in phase plane analysis: some basic models and problems.