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Nonlinear Water Waves

Cetraro, Italy 2013

  • Book
  • © 2016

Overview

Authors:
  1. Adrian Constantin

    1. Faculty of Mathematics, University of Vienna, Vienna, Austria

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  2. Joachim Escher

    1. Inst. for Applied Mathematics, Gottfried Wilhelm Leibniz University Nie, Hannover, Germany

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  3. Robin Stanley Johnson

    1. School of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne, United Kingdom

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  4. Gabriele Villari

    1. Department of Mathematics “Ulisse Dini”, University of Florence, Florence, Italy

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Editors:
  1. Adrian Constantin

    1. Faculty of Mathematics, University of Vienna, Vienna, Austria

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  • 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

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2158)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-vii
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  2. Exact Travelling Periodic Water Waves in Two-Dimensional Irrotational Flows

    • Adrian Constantin
    Pages 1-82

  3. Breaking Water Waves

    • Joachim Escher
    Pages 83-119

  4. Asymptotic Methods for Weakly Nonlinear and Other Water Waves

    • Robin Stanley Johnson
    Pages 121-196

  5. A Survival Kit in Phase Plane Analysis: Some Basic Models and Problems

    • Gabriele Villari
    Pages 197-228

  6. Back Matter

    Pages 229-230
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Keywords

About this book

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.

Authors, Editors and Affiliations

  • Faculty of Mathematics, University of Vienna, Vienna, Austria

    Adrian Constantin, Adrian Constantin

  • Inst. for Applied Mathematics, Gottfried Wilhelm Leibniz University Nie, Hannover, Germany

    Joachim Escher

  • School of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne, United Kingdom

    Robin Stanley Johnson

  • Department of Mathematics “Ulisse Dini”, University of Florence, Florence, Italy

    Gabriele Villari

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