Lecture Notes in Physics

New Approaches to Nonlinear Waves

Editors: Tobisch, Elena (Ed.)

  • Written by leading experts in nonlinear waves
  • Brings together theoretical, numerical and experimental approaches
  • With applications to real physical problems
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  • ISBN 978-3-319-20690-5
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Softcover $59.99
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About this book

The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book.

Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3).

In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5).

The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system.

The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments.

All the chapters are illustrated by ample constructive examples demonstrating the applicability of these novel methods and approaches to a wide class of evolutionary dispersive PDEs, e.g. equations from Benjamin-Oro, Boussinesq, Hasegawa-Mima,  KdV-type,  Klein-Gordon, NLS-type, Serre,  Shamel , Whitham and Zakharov.

This makes the book interesting for professionals in the fields of nonlinear physics, applied mathematics and fluid mechanics as well as students who are studying these subjects. The book can also be used as a basis for a one-semester lecture course in applied mathematics or mathematical physics.

 

 

Table of contents (8 chapters)

  • Introduction

    Tobisch, Elena

    Pages 1-19

  • The Effective Equation Method

    Kuksin, Sergei (et al.)

    Pages 21-41

  • On the Discovery of the Steady-State Resonant Water Waves

    Liao, Shijun (et al.)

    Pages 43-82

  • Modulational Instability in Equations of KdV Type

    Bronski, Jared C. (et al.)

    Pages 83-133

  • Modulational Instability and Rogue Waves in Shallow Water Models

    Grimshaw, R. (et al.)

    Pages 135-151

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-319-20690-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-3-319-20689-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
New Approaches to Nonlinear Waves
Editors
  • Elena Tobisch
Series Title
Lecture Notes in Physics
Series Volume
908
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-20690-5
DOI
10.1007/978-3-319-20690-5
Softcover ISBN
978-3-319-20689-9
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XV, 298
Number of Illustrations and Tables
50 b/w illustrations, 15 illustrations in colour
Topics