Non-Linear Waves in Dispersive Media (eBook)
198 Seiten
Elsevier Science (Verlag)
978-1-4831-8715-0 (ISBN)
Non-Linear Waves in Dispersive Media introduces the theory behind such topic as the gravitational waves on water surfaces. Some limiting cases of the theory, wherein proof of an asymptotic class is necessary and generated, are also provided. The first section of the book discusses the notion of linear approximation. This discussion is followed by some samples of dispersive media. Examples of stationary waves are also examined. The book proceeds with a discussion of waves of envelopes. The concept behind this subject is from the application of the methods of geometrical optics to non-linear theory. A section on non-linear waves with slowly varying parameters is given at the end of the book, along with a discussion of the evolution of electro-acoustic waves in plasma with negative dielectric permittivity. The gravitational waves on fluid surfaces are presented completely. The text will provide valuable information for physicists, mechanical engineers, students, and researchers in the field of optics, acoustics, and hydrodynamics.
Front Cover 1
Non-Linear Waves in Dispersive Media 4
Copyright Page 5
Table of Contents 6
PREFACE 8
INTRODUCTION 10
Chapter 1. LINEAR APPROXIMATION 14
§ 2 General Solution of the Linearized Equations 14
§ 3 Linearized Korteweg–de Vries Equation 17
Chapter 2. EXAMPLES OF DISPERSIVE MEDIA 21
§ 4 Gravitational Waves on Fluid Surfaces 21
§ 5 The Boussinesq Equation 23
§ 6 Ion-sound Waves in Unmagnetized Plasma 28
§ 7 Non-linear Waves in Magnetized Plasma 31
§ 8 Non-linear Electromagnetic Waves in Isotropie Dielectrics 38
§ 9 Sound Waves with Dispersion 45
Chapter 3. NON-LINEAR STATIONARY WAVES 50
§ 10 Steady Solutions of the Boussinesq Equations 50
§ 11 Stationary Waves Propagating Transversely to the Magnetic Field in Rarefied Plasma (34–37, 3) 57
§ 12 Other Examples of Stationary Waves 60
Chapter 4. NON-LINEAR WAVES IN WEAKLY DISPERSIVE MEDIA 66
§ 13 The Burgers Equation 66
§ 14 Solution of the Burgers Equation 72
§15 The Korteweg–de Vries Equation 75
§ 16 Conservation Laws for the Korteweg-de Vries Equation 79
§ 17 General Pattern of the Evolution of Initial Perturbations in Weakly Dispersive Media 82
§ 18 Analytical Solution of the Korteweg-de Vries Equation 85
§ 19 Asymptotic Expressions for the Amplitudes of Solitons and "Tails" for Large Values of s 93
§ 20 Self-similar Solutions of the Korteweg-de Vries Equation 96
§ 21 Quasi-linear Solutions of the Korteweg-de Vries Equation 98
§ 22 Flow Around a Thin Body in a Dispersive Medium 105
§ 23 Shock Waves in Dispersive Media 114
Chapter 5. WAVES OF ENVELOPES 119
§ 24 Non-linear Geometrical Optics 119
§ 25 Instability Criteria for Stationary Waves 122
§ 26 Evolution of the Wave Envelopes in the "Hydrodynamic Approximation" 125
§ 27 Non-linear Parabolic Equation 133
§ 28 Self-modulation of Waves (Modulational Instability) 141
§ 29 Self-focusing and Self-channelling of Waves 148
§ 30 Electro-acoustic Waves in Plasma 154
APPENDIX A: NON-LINEAR WAVES WITH SLOWLY VARYING PARAMETERS (ADIABATIC APPROXIMATION OF WHITHAM) 160
A 1 Variation Principle 160
A 2 Adiabatic Invariants 165
A 3 Non-linear Geometrical Optics 169
APPENDIX B: EVOLUTION OF ELECTRO-ACOUSTIC WAVES IN PLASMA WITH NEGATIVE DIELECTRIC PERMITTIVITY 171
B 1 Boundary Conditions 171
B 2 Excitation and Evolution of Electro-acoustic Waves 174
B 3 Solution of the Boundary-value Problem 183
B 4 General Solution of the Fundamental Equations 187
REFERENCES 190
INDEX 194
OTHER TITLES IN THE SERIES IN NATURAL PHILOSOPHY 198
Erscheint lt. Verlag | 22.1.2016 |
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Sprache | englisch |
Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Mechanik |
Technik ► Maschinenbau | |
ISBN-10 | 1-4831-8715-2 / 1483187152 |
ISBN-13 | 978-1-4831-8715-0 / 9781483187150 |
Haben Sie eine Frage zum Produkt? |
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