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| ERYK INFELD was born in Toronto in 1940. In 1950 he left Canada for Poland, as his father was, Polish (the scientist Leopole Infeld, best known for his work with Einstein). He graduated from both Warsaw University (physics) and Cambridge University (mathematics). He is a professor of nonlinear dynamics in Warsaw and has visited Cambridge University, University College London, Culham Laboratories, Warwick University (Royal Society Visitor) and the.. << 查看详细 |
| 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 cma diagrams 2.4 instabilities 2.5 the vlasov equation 2.6 weak instabilities exercises 3 convective and non-convective instabilities; group velocity in unstable media 3.1 introduction 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 amplitude ion acoustic waves in an unmagnetized plasma 5.2.3 weak amplitude ion acoustic waves in a magnetized plasma 5.3 weakly nonlinear waves 5.3.1 spreading, splitting and instabilities 5.3.2 the story of deep water waves 5.3.3 mystery of the missing term 5.3.4 dynamics of a wavepacket 5.3.5 some generalizations 5.4 a general look at two families of model equations 5.5 a natural extension to finite amplitude waves due to hayes 5.6 temporal development of instabilities 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 6.2.1 one stationary wave in a dissipationless medium 6.2.2 a two-fluid layer soliton pair 6.2.3 weak ion acoustic shock waves in a collisional plasma 6.2.4 solitons generated by laser fields 6.2.5 solitons and domains in dipole chains 6.2.6 discrete equations 6.3 bernstein-greene-kruskal waves 6.3.1 statistical description of a plasma and bgk waves 6.3.2 no trapped particles 6.3.3 various limits 6.3.4 trapped particle equilibria 6.3.5 stability; subsequent developments 6.4 lagrangian methods 6.5 lagrangian interpolation exercises 7 cartesian solitons in one and two space dimensions 7.1 introduction 7.2 the direct method 7.3 constants of motion 7.4 inverse scattering method 7.5 backlund transformations 7.6 entr'acte .. 7.7 breathers and boundary effects 7.8 experimental evidence 7.9 plane soliton interaction in two space dimensions 7.9.1 introducing the trace method 7.9.2 one and two sotiton solutions 7.9.3 some other developments and summary 7.10 integrable equations in two space dimensions as treated by the zakharov-shabat method 7.10.1 lax pairs and the pdes they represent 7.10.2 extension to x,y,t 7.10.3 how to proceed from the lax pair to the general solution 7.10.4 an example: the kadomtsev-petviashvili equation 7.11 summary exercises 8 evolution and stability of initially one-dimensional waves and solitons 8.1 a brief historical survey of large amplitude nonlinear wave studies 8.1.1 solitons 8.1.2 water waves are unstable 8.1.3 the geometrical optics limit 8.1.4 more recent results 8.1.5 what the remainder of chapter 8 is about 8.2 four methods as illustrated by the nonlinear klein-gordon equation 8.2.1 whitham i 8.2.2 whitham ii 8.2.3 k expansion 8.2.4 hayes 8.3 higher dimensional dynamics 8.3.1 kadomtsev-petviashvili as analysed by whitham ii 8.3.2 various limits 8.3.3 common features of the weak amplitude and soliton limits for ψ=0 8.3.4 group velocity 8.3.5 zakharov-kuznetsov as analysed by k expansion 8.3.6 the variational method 8.4 a more physical approach leading to an assessment of models 8.4.1 form of the waves considered 8.4.2 unmagnetized plasmas, ftc= 0 8.4.3 magnetized plasmas, ωc ] 0 8.5 dynamics of nonlinear wave, shock and soliton solutions to the cubic nonlinear schrodinger equation 8.5.1 results of a general stability calculation 8.5.2 one-dimensional dynamics: ψ= 0 8.5.3 oblique and perpendicular propagation of perturbations 8.6 the direct k method 8.6.1 transverse instability of zakharov-kuznetsov solitons 8.6.2 the cahn-hilliard equation 8.7 some general conclusions and possible future lines of investigation exercises 9 cylindrical and spherical solitons in plasmas and other media 9.1 interest in higher dimensional plasma solitons 9.2 unidirectional cylindrical and spherical ion acoustic solitons 9.2.1 model equations in non-cartesian geometry 9.2.2 cylindrical soliton equations ci and cii 9.2.3 spherical solitons 9.2.4 summary 9.3 properties of unidirectional soliton equations 9.3.1 integrability by inverse scattering 9.3.2 conservation laws 9.4 soliton solutions as compared with numerics and experiments 9.4.1 exact solutions to ci 9.4.2 initial value problem and experiments 9.4.3 reflection from the axis (centre) 9.4.4 models 9.4.5 stability of cylindrical solitons 9.5 langmuir solitons 9.5.1 integrability 9.5.2 stability of langmuir solitons 9.6 interacting solitons and some conclusions 9.7 epilogue. some other examples of spherical and cylindrical solitons exercises 10 soliton metamorphosis 10.1 the next step in investigating soliton behaviour 10.2 decay of line kpi solitons in two dimensions 10.3 decay of 2d solitons in three dimensions 10.3.1 2d solitons perturbed perpendicular to the motion 10.3.2 2d solitons perturbed parallel to the velocity 10.4 conclusions exercises 11 non-coherent phenomena 11.1 introduction 11.2 bifurcation sequences and chaos 11.3 flows and maps 11.4 strange attractors 11.5 effect of external noise 11.6 experimental evidence for strange attractors 11.7 other theories of turbulence 11.8 conclusions exercises appendices a1 parameter stretching as suggested by the linear dispersion relations a1.1 ion acoustic waves in an unmagnetized plasma, ωc= 0 al.2 magnetized plasmas, ωc ] 0 a2 relation between the trace method and the inverse scattering method a3 some formulae for perturbed nonlinear ion acoustic waves and solitons a3.1 no magnetic field a3.2 ωc ] 0 a4 colliding soliton theory a5 a model equation for spherical solitons a6 stability calculation for 2d kpi soliton in 3d references author index subject index colour plates between pages 300-301 ... |
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