《孤子波》求取 ⇩
作者 | M.REMOISSENET著 编者 |
---|---|
出版 | 北京:世界图书出版公司北京公司 |
参考页数 | 260 ✅ 真实服务 非骗流量 ❤️ |
出版时间 | 1999(求助前请核对) 目录预览 |
ISBN号 | 7506241056 — 违规投诉 / 求助条款 |
PDF编号 | 81040038(学习资料 勿作它用) |
求助格式 | 扫描PDF(若分多册发行,每次仅能受理1册) |
1Basic Concepts and the Discovery of Solitons1
1.1 A look at linear and nonlinear signatures1
1.2 Discovery of the solitary wave3
1.3 Discovery of the soliton6
1.4 The soliton concept in physics10
2Linear Waves in Electrical Transmission Lines12
2.1 Linear nondispersive waves12
2.2Sinusoidal-wave characteristics15
2.2.1 Wave energy density and power18
2.3 The group-velocity concept19
2.4 Linear dispersive waves21
2.4.1 Dispersive transmission lines21
2.4.2Electrical network23
2.4.3 The weakly dispersive limit26
2.5 Evolution of a wavepacket envelope27
2.6 Dispersion-induced wavepacket broadening31
Appendix 2A.General solution for the envelope evolution34
Appendix 2B. Evolution of the envelope of a Gaussian wavepacket35
3Solitons in Nonlinear Transmission Lines37
3.1 Nonlinear and dispersionless transmission lines37
3.2 Combined effects of dispersion and nonlinearity41
3.3 Electrical solitary waves and pulse solitons42
3.4 Laboratory experiments on pulse solitons46
3.4.1Experimental arrangement46
3.4.2 Series of experiments48
3.5 Experiments with a pocket version of the electrical network52
3.6 Nonlinear transmission lines in the microwave range56
Appendix 3A.Calculation of the effect of nonlinearity on wave propagation58
Appendix 3B.Derivation of the solitary-wave solution60
Appendix 3C.Derivation of the KdV equation and its soliton solution62
Appendix 3D.Details of the electronics:switch driver and pulse generator64
4More on Transmission-Line Solitons65
4.1 Lattice solitons in the electrical Toda network65
4.1.1Lattice solitons67
4.2Experiments on lattice solitons68
4.2.1 Collisions of two lattice solitons moving in opposite directions70
4.2.2 The Fermi-Pasta-Ulam recurTence phenomenon70
4.3 Periodic wavetrains in transmission lines71
4.3.1 The solitary wave limit and sinusoidal limit of the cnoidal wave72
4.4Modulated waves and the nonlinear dispersion relation72
4.5Envelope and hole solitons74
4.5.1 Experiments on envelope and hole solitons76
4.6 Modulational instability77
4.7 Laboratory experiments on modulational instability82
4.7.1Model equations82
4.7.2 Experiments84
4.8 Modulational instability of two coupled waves86
Appendix 4A.Periodic wavetrain solutions88
Appendix 4B.The Jacobi elliptic functions90
4B.1 Asymptotic limits91
4B.2 Derivatives and integrals93
Appendix 4C.Envelope and hole soliton solutions93
5Hydrodynamic Solitons98
5.1Equations for surface water waves98
5.1.1 Reduced fluid equations99
5.2 Small-amplitude surface gravity waves100
5.3 Linear shallow-and deep-water waves103
5.3.1Shallow-waterwaves103
5.3.2 Deep-water waves104
5.4 Surface-tension effects:capillary waves105
5.5 Solitons in shallow water107
5.6Experiments on solitons in shallow water110
5.6.1 Experimental arrangement111
5.6.2 Experiments111
5.7Stokes waves and soliton wavepackets in deep water115
5.7.1 Stokes waves115
5.7.2 Soliton wavepackets116
5.7.3 Experiments on solitons in deep water117
5.8 Experiments on modulational instability in deep water118
Appendix 5A.Basic equations of fluid mechanics121
5A.1 Conservation of mass121
5A.2 Conservation of momentum123
5A.3 Conservation of entropy124
Appendix 5B.Basic definitions and approximations124
5B.1 Streamline124
5B.2 Irrotational and incompressible flow125
5B.3 Two-dimensional flow:the stream function126
5B.4 Boundary conditions128
5B.5 Surface tension129
Appendix 5C.Derivation of the KdV equation:the perturbative approach130
Appendix 5D.Derivation of the nonlinear dispersion relation133
Appendix 5E.Details of the probes and the electronics136
6Mechanical Solitons137
6.1An experimental mechanical transmisssion line137
6.1.1 General description of the line137
6.1.2 Construction of the line139
6.2Mechanical kink solitons139
6.2.1 Linear waves in the low-amplitude limit140
6.2.2 Large amplitude waves:kink solitons141
6.2.3 Lorentz contraction of the kink solitons143
6.3 Particle properties of the kink solitons145
6.4 Kink-kink and kink-antikink collisions146
6.5 Breather solitons148
6.6 Experiments on kinks and breathers150
6.7 Helical waves,or kink array151
6.8 Dissipative effects153
6.9 Envelope solitons155
6.10 Pocket version of the pendulum chain,lattice effects157
Appendix 6A.Kink soliton and antikink soliton solutions159
Appendix 6B.Calculation of the energy and the mass of a kink soliton160
Appendix 6C.Solutions for kink-kink and kink-antikink collisions,and breathers161
6C.1 Kink solutions163
6C.2 Kink-kink collisions163
6C.3 Breather solitons164
6C.4 Kink-antikink collision165
Appendix 6D.Solutions for helical waves166
7Fluxons in Josephson Transmission Lines168
7.1The Josephson effect in a short junction168
7.1.1 The small Josephson junction169
7.2 The long Josephson junction as a transmission line171
7.3 Dissipative effects175
7.4Experimental observations of fluxons177
7.4.1 Indirect observation177
7.4.2 Direct observation178
7.4.3 Latrice effects180
Appendix 7A.Josephson equations180
8Solitons in Optical Fibers182
8.1Optical-fiber characteristics182
8.1.1 Linear dispersive effects183
8.1.2 Nonlinear effects185
8.1.3 Effect of losses186
8.2 Wave-envelope propagation187
8.3Bright and dark solitons189
8.3.1 Bright solitons190
8.3.2 Dark solitons192
8.4 Experiments on optical solitons193
8.5 Perturbations and soliton communications195
8.5.1Effect of losses195
8.5.2 Soliton communications196
8.6 Modulational instability of coupled waves197
8.7 A look at quantum optical solitons198
Appendix 8A.Electromagnetic equations in a nonlinear medium199
9The Soliton Concept in Lattice Dynamics202
9.1 The one-dimensional lattice in the continuum approximation202
9.2 The quasi-continuum approximation for the monatomic lattice207
9.3 The Toda lattice209
9.4 Envelope solitons and localized modes210
9.5 The one-dimensional lattice with transverse nonlinear modes212
9.6 Motion of dislocations in a one-dimensional crystal215
9.7 The one-dimensional lattice model for structural phase transitions216
9.7.1The order-disorder transition218
9.7.2 The displacive transition219
Appendix 9A.Solutions for transverse displacements221
Appendix 9B.Kink soliton or domain-wall solutions223
10A Look at Some Remarkable Mathematical Techniques225
10.1 Lax equations and the inverse scattering transform method225
10.1.1 The Fourier-transform method for linear equations226
10.1.2 The Lax pair for nonlinear evolution equations227
10.2 The KdV equation and the spectral problem229
10.3 Time evolution of the scattering data230
10.3.1 Discrete eigenvalues230
10.3.2Continuous spectrum232
10.4 The inverse scattering problem233
10.4.1 Discrete spectrum only:soliton solution234
10.5Response of the KdV model to an initial disturbance236
10.5.1 The delta function potential236
10.5.2 The rectangular potential well237
10.5.3 The sech-squared potential well237
10.6 The inverse scattering transform for the NLS equation238
10.7 The Hirota method for the KdV equation239
10.8 The Hirota method for the NLS equation243
References247
Subject Index259
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