Overview
- Written by leading experts in nonlinear waves
- Brings together theoretical, numerical and experimental approaches
- With applications to real physical problems
Part of the book series: Lecture Notes in Physics (LNP, volume 908)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
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.
Editors and Affiliations
Bibliographic Information
Book Title: New Approaches to Nonlinear Waves
Editors: Elena Tobisch
Series Title: Lecture Notes in Physics
DOI: https://doi.org/10.1007/978-3-319-20690-5
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-20689-9Published: 29 August 2015
eBook ISBN: 978-3-319-20690-5Published: 19 August 2015
Series ISSN: 0075-8450
Series E-ISSN: 1616-6361
Edition Number: 1
Number of Pages: XV, 298
Number of Illustrations: 50 b/w illustrations, 15 illustrations in colour
Topics: Theoretical, Mathematical and Computational Physics, Classical and Continuum Physics, Complex Systems, Geophysics and Environmental Physics, Statistical Physics and Dynamical Systems