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Nonlinear Water Waves

An Interdisciplinary Interface

  • Book
  • © 2019

Overview

Editors:
  1. David Henry

    1. School of Mathematical Sciences, University College Cork, Cork, Ireland

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  2. Konstantinos Kalimeris

    1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

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  3. Emilian I. Părău

    1. School of Mathematics, University of East Anglia, Norwich, UK

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  4. Jean-Marc Vanden-Broeck

    1. Department of Mathematics, University College London, London, UK

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  5. Erik Wahlén

    1. Centre for Mathematical Sciences, Lund University, Lund, Sweden

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  • Interdisciplinary approach to research in nonlinear water waves featuring contributions from mathematics, physics and engineering
  • Presents a fascinating mixture of material ranging from survey articles to new research results
  • Offers an extensive overview of the state of the art of the research field in nonlinear water waves, while also posing a number of interesting and important open questions
  • Encourages more research in this area

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Modeling Surface Waves Over Highly Variable Topographies

    • André Nachbin
    Pages 1-18

  3. Global Diffeomorphism of the Lagrangian Flow-map for a Pollard-like Internal Water Wave

    • Mateusz Kluczek, Adrián Rodríguez-Sanjurjo
    Pages 19-34

  4. The Unified Transform and the Water Wave Problem

    • A. S. Fokas, K. Kalimeris
    Pages 35-52

  5. HOS Simulations of Nonlinear Water Waves in Complex Media

    • Philippe Guyenne
    Pages 53-69

  6. Stokes Waves in a Constant Vorticity Flow

    • Sergey A. Dyachenko, Vera Mikyoung Hur
    Pages 71-86

  7. Integrable Models of Internal Gravity Water Waves Beneath a Flat Surface

    • Alan C. Compelli, Rossen I. Ivanov, Tony Lyons
    Pages 87-108

  8. Numerical Simulations of Overturned Traveling Waves

    • Benjamin F. Akers, Matthew Seiders
    Pages 109-122

  9. A Model for the Periodic Water Wave Problem and Its Long Wave Amplitude Equations

    • Roman Bauer, Patrick Cummings, Guido Schneider
    Pages 123-138

  10. On Recent Numerical Methods for Steady Periodic Water Waves

    • Dominic Amann
    Pages 139-149

  11. Nonlinear Wave Interaction in Coastal and Open Seas: Deterministic and Stochastic Theory

    • Raphael Stuhlmeier, Teodor Vrecica, Yaron Toledo
    Pages 151-181

  12. Gravity-Capillary and Flexural-Gravity Solitary Waves

    • Emilian I. Părău, Jean-Marc Vanden-Broeck
    Pages 183-199

  13. A Method for Identifying Stability Regimes Using Roots of a Reduced-Order Polynomial

    • Olga Trichtchenko
    Pages 201-216
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Keywords

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.


Editors and Affiliations

  • School of Mathematical Sciences, University College Cork, Cork, Ireland

    David Henry

  • Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Konstantinos Kalimeris

  • School of Mathematics, University of East Anglia, Norwich, UK

    Emilian I. Părău

  • Department of Mathematics, University College London, London, UK

    Jean-Marc Vanden-Broeck

  • Centre for Mathematical Sciences, Lund University, Lund, Sweden

    Erik Wahlén

Bibliographic Information

  • Book Title: Nonlinear Water Waves

  • Book Subtitle: An Interdisciplinary Interface

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

  • Series Title: Tutorials, Schools, and Workshops in the Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-030-33536-6

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-33535-9Published: 06 December 2019

  • Softcover ISBN: 978-3-030-33538-0Published: 06 December 2020

  • eBook ISBN: 978-3-030-33536-6Published: 27 November 2019

  • Series ISSN: 2522-0969

  • Series E-ISSN: 2522-0977

  • Edition Number: 1

  • Number of Pages: X, 218

  • Number of Illustrations: 21 b/w illustrations, 32 illustrations in colour

  • Topics: Partial Differential Equations

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