Nonlinear Water Waves

An Interdisciplinary Interface

  • David Henry
  • Konstantinos Kalimeris
  • Emilian I. Părău
  • Jean-Marc Vanden-Broeck
  • Erik Wahlén

Table of contents

  1. Front Matter
    Pages i-x
  2. Mateusz Kluczek, Adrián Rodríguez-Sanjurjo
    Pages 19-34
  3. A. S. Fokas, K. Kalimeris
    Pages 35-52
  4. Sergey A. Dyachenko, Vera Mikyoung Hur
    Pages 71-86
  5. Alan C. Compelli, Rossen I. Ivanov, Tony Lyons
    Pages 87-108
  6. Benjamin F. Akers, Matthew Seiders
    Pages 109-122
  7. Roman Bauer, Patrick Cummings, Guido Schneider
    Pages 123-138
  8. Raphael Stuhlmeier, Teodor Vrecica, Yaron Toledo
    Pages 151-181
  9. Emilian I. Părău, Jean-Marc Vanden-Broeck
    Pages 183-199

About this book


The motion of water is governed by a set of mathematical equations which are extremely complicated and intractable. This is not surprising when one considers the highly diverse and intricate physical phenomena which may be exhibited by a given body of water. Recent mathematical advances have enabled researchers to make major progress in this field, reflected in the topics featured in this volume.

Cutting-edge techniques and tools from mathematical analysis have generated strong rigorous results concerning the qualitative and quantitative physical properties of solutions of the governing equations. Furthermore, accurate numerical computations of fully-nonlinear steady and unsteady water waves in two and three dimensions have contributed to the discovery of new types of waves. Model equations have been derived in the long-wave and modulational regime using Hamiltonian formulations and solved numerically.

This book brings together interdisciplinary researchers working in the field of nonlinear water waves, whose contributions range from survey articles to new research results which address a variety of aspects in nonlinear water waves. It is motivated by a workshop which was organised at the Erwin Schrödinger International Institute for Mathematics and Physics in Vienna, November 27-December 7, 2017. The key aim of the workshop was to describe, and foster, new approaches to research in this field. This is reflected in the contents of this book, which is aimed to stimulate both experienced researchers and students alike.


water waves nonlinear analysis partial differential equations numerical computations interdisciplinary

Editors and affiliations

  • David Henry
    • 1
  • Konstantinos Kalimeris
    • 2
  • Emilian I. Părău
    • 3
  • Jean-Marc Vanden-Broeck
    • 4
  • Erik Wahlén
    • 5
  1. 1.School of Mathematical SciencesUniversity College CorkCorkIreland
  2. 2.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK
  3. 3.School of MathematicsUniversity of East AngliaNorwichUK
  4. 4.Department of MathematicsUniversity College LondonLondonUK
  5. 5.Centre for Mathematical SciencesLund UniversityLundSweden

Bibliographic information

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