內容簡介

This revised and updated second edition.of a，highly successful book is the only text at this level to embrace a universai approach to three major developments in classical physics; namely nonlinear waves，solitons and chaos。The authors now include new material on biology and laser theory，and go on to discuss important recent developments such as soliton metamorphosis。

A comprehensive treatment of basic plasma and fluid configurations and instabilities is followed by a study of the relevant nonlinear structures。Examples of these are coherent entities like nonlinear waves and solitons，as well as the incoherent structures associated with chaos。The first part of the book is a self-contained introduction to general topics associated with nonlinear graduate physics，and would be accessible to final-year undergraduates and beginning graduate students。The remainder of the book，for example the treatment of cylindrical solitons，is more advanced and will have a wide appeal to specialists in a number of branches of physics。Each chapter concludes with a set of problems...

This text will be particularly valuable for students taking courses in nonlinear aspects of physics。In general，it will。be of value to final-year undergraduates and beginning graduate students studying fluid dynamics，plasma physics or applied mathematics。
 

目錄

Foreword to the first edition
Foreword to the second edition
1 Introduction
1.1 Occurrence of nonlinear waves and instabilities in Nature
1.1.1 Nonlinear phenomena in our everyday experience
1.1.2 Nonlinear phenomena in the laboratory
1.2 Universal wave equations
1.2.1 The Korteweg-de Vries and Kadomtsev-Petviashvili equations and a first look at solitons
1.2.2 The nonlinear Schr6dingcr equation
1.2.3 Nonlinear optics
1.3 What is a plasma？
1.4 Wave modes on a water surface
1.4.1 Mathematicaltheory
1.4.2 Comments
1.5 Linear stability analysis and its limitations
1.6 Nonlinear structures
1.6.1 Coherent structures and pattern formation
1.7 Contents of Chapters 2-11
2 Linear waves and instabilities in infinite media
2.1 Introduction
2.2 Plasma waves
2.3 CMM diagrams
2.4 Instabilities
2.5 The Vlasov equations
2.6 Weak instabilites
Exercises
3 Convective and non-convective instabilities;guoup velcoity in unstable media
4 A first look at surface waves and instabilities
5 Model equations for small amplitued waves and solitons;weakly nonlinear theory
6 Exact methods for fully nonlinear waves and solitons
7 Cartesian solitons in ond the two space dimensions
8 Evolution and stability of initially one-dimensional waves and solitons
9 Cylindrical and spherical solitons in palsmas and other media
10 Soliton metamorphosis
11 Non-coerent phenomena
Appendices
References
Author index
Subject index
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