Nonlinear Waves

doi:10.1017/CBO9780511569500

Nonlinear Waves

The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.

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Nonlinear Waves

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Contents

Frontmatter
pp i-ii

Contents
pp iii-iv

Preface
pp v-viii

Part I - Nonlinear Waves in Fluids

1 - Towards the Analytic Description of Overturning Waves
pp 1-24

2 - The Korteweg-de Vries Equation and Related Problems in Water Wave Theory
pp 25-43

3 - Solitary Waves in Slowly Varying Environments: Long Nonlinear Waves
pp 44-68

4 - Nonlinear Waves in a Channel
pp 69-83

5 - Soliton Behaviour in Models of Baroclinic Instability
pp 84-99

6 - Waves and Wave Groups in Deep Water
pp 100-115

7 - Two-and Three-Wave Resonance
pp 116-132

Part II - Nonlinear Waves in Plasmas

8 - Nonlinear Electromagnetic Waves in Flowing Plasma
pp 133-161

9 - Superluminous Waves in Plasmas
pp 162-176

10 - Electrostatic Ion Cyclotron Waves and Ion Heating in a Magnetic Field
pp 177-196

11 - Solitons in Plasma Physics
pp 197-220

12 - A Theory for the Propagation of Slowly Varying Nonlinear Waves in a Non-Uniform Plasma
pp 221-244

Part III - Solitons, Inverse Scattering Transform, and Nonlinear Waves in Physics

13 - On the Inverse Scattering Transform in Two Spatial and One Temporal Dimensions
pp 245-267

14 - Linear Evolution Equations Associated with Isospectral Evolutions of Differential Operators
pp 268-284

15 - Inverse Scattering for the Matrix Schrö Equation with Non-Hermitian Potential
pp 285-297

16 - A General nth Order Spectral Transform
pp 298-307

17 - Recurrence Phenomena and the Number of Effective Degrees of Freedom in Nonlinear Wave Motions
pp 308-325

18 - Action-Angle Variables in the Statistical Mechanics of the Sine-Gordon Field
pp 326-355

Index
pp 356-360

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Nonlinear Waves

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