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| 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 3.1 Introdction 3.2 Kinematics of unstable wavepackets 3.3 Moving coordinate systems 3.4 Higher dimensional systems 3.5 Summary Exercise 4 A first look at surface waves and instabilities 4.1 Introduction 4.2 Simple surface waves 4.3 The Rayleigh-Taylor instability 4.4 The Kelvin-Helmholtz instability 4.5 Solid-liquid interface instabilities 4.6 A first look at gravity wave instabilities 4.6.1 The small amplitude onset of wave instability 4.6.2 Further numerical results 4.7 Summary Exercises 5 Model equations for small amplitude waves and solitons; weakly nonlinear theory 5.1 Introduction 5.1.1 Some physical equations ask for surgery 5.1.2 Examples 5.2 A few model equations as derived by introducing a small parameter 5.2.1 Shallow water， weak amplitude gravity waves 5.2.2 Weak amplitudeion acoustic wavesin an unmagnetized plasma 5.2.3 Weak amplitudeion acoustic waves in a magnetized plasma 5.3 Weakly nonlinear waves 5.3.1 Spreading,splitting and instabilities 5.3.2 The story ofdeep water waves 5.3.3 Mystery of the missing term 5.3.4 Dynamics ofa wavepacket 5.3.5 Somegeneralizations 5.4 A generallook at two families of model equations 5.5 A natural extension to finite amplitude waves due to Hayes 5.6 Temporal development ofinstabilities and wave-wave coupling 5.7 Concluding remarks Exercises 6 Exact methods for fully nonlinear waves and solitons 6.1 Introduction 6.2 Phase plane analysis and other methods …… 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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