Nonlinear Water Waves

Cetraro, Italy 2013

  • Adrian Constantin
  • Joachim Escher
  • Robin Stanley Johnson
  • Gabriele Villari
  • Adrian Constantin

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

Also part of the C.I.M.E. Foundation Subseries book sub series (LNMCIME, volume 2158)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Joachim Escher
    Pages 83-119
  3. Back Matter
    Pages 229-230

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. 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.


76B15, 35Q35, 34C05 Water waves free boundary nonlinear, particle paths model equations

Authors and affiliations

  • Adrian Constantin
    • 1
  • Joachim Escher
    • 2
  • Robin Stanley Johnson
    • 3
  • Gabriele Villari
    • 4
  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Inst. for Applied MathematicsGottfried Wilhelm Leibniz University NieHannoverGermany
  3. 3.School of Mathematics and StatisticsUniversity of NewcastleNewcastle upon TyneUnited Kingdom
  4. 4.Department of Mathematics “Ulisse Dini”University of FlorenceFlorenceItaly

Editors and affiliations

  • Adrian Constantin
    • 1
  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-31461-7
  • Online ISBN 978-3-319-31462-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking