Karpman / Ter Haar Non-Linear Waves in Dispersive Media

International Series of Monographs in Natural Philosophy
1. Auflage 2016
ISBN: 978-1-4831-8715-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 198 Seiten, Web PDF

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.

Autoren/Hrsg.

Karpman, V. I.

Ter Haar, D.

Inhaltsverzeichnis

1;Front Cover;1
2;Non-Linear Waves in Dispersive Media;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;8
6;INTRODUCTION;10
7;Chapter 1. LINEAR APPROXIMATION;14
7.1;§ 2 General Solution of the Linearized Equations;14
7.2;§ 3 Linearized Korteweg–de Vries Equation;17
8;Chapter 2. EXAMPLES OF DISPERSIVE MEDIA;21
8.1;§ 4 Gravitational Waves on Fluid Surfaces;21
8.2;§ 5 The Boussinesq Equation;23
8.3;§ 6 Ion-sound Waves in Unmagnetized Plasma;28
8.4;§ 7 Non-linear Waves in Magnetized Plasma;31
8.5;§ 8 Non-linear Electromagnetic Waves in Isotropie Dielectrics;38
8.6;§ 9 Sound Waves with Dispersion;45
9;Chapter 3. NON-LINEAR STATIONARY WAVES;50
9.1;§ 10 Steady Solutions of the Boussinesq Equations;50
9.2;§ 11 Stationary Waves Propagating Transversely to the Magnetic Field in Rarefied Plasma (34–37, 3);57
9.3;§ 12 Other Examples of Stationary Waves;60
10;Chapter 4. NON-LINEAR WAVES IN WEAKLY DISPERSIVE MEDIA;66
10.1;§ 13 The Burgers Equation;66
10.2;§ 14 Solution of the Burgers Equation;72
10.3; §15 The Korteweg–de Vries Equation;75
10.4;§ 16 Conservation Laws for the Korteweg-de Vries Equation;79
10.5;§ 17 General Pattern of the Evolution of Initial Perturbations in Weakly Dispersive Media;82
10.6;§ 18 Analytical Solution of the Korteweg-de Vries Equation;85
10.7;§ 19 Asymptotic Expressions for the Amplitudes of Solitons and "Tails" for Large Values of s;93
10.8;§ 20 Self-similar Solutions of the Korteweg-de Vries Equation;96
10.9;§ 21 Quasi-linear Solutions of the Korteweg-de Vries Equation;98
10.10;§ 22 Flow Around a Thin Body in a Dispersive Medium;105
10.11;§ 23 Shock Waves in Dispersive Media;114
11;Chapter 5. WAVES OF ENVELOPES;119
11.1;§ 24 Non-linear Geometrical Optics;119
11.2;§ 25 Instability Criteria for Stationary Waves;122
11.3;§ 26 Evolution of the Wave Envelopes in the "Hydrodynamic Approximation";125
11.4;§ 27 Non-linear Parabolic Equation;133
11.5;§ 28 Self-modulation of Waves (Modulational Instability);141
11.6;§ 29 Self-focusing and Self-channelling of Waves;148
11.7;§ 30 Electro-acoustic Waves in Plasma;154
12;APPENDIX A: NON-LINEAR WAVES WITH SLOWLY VARYING PARAMETERS (ADIABATIC APPROXIMATION OF WHITHAM);160
12.1;A 1 Variation Principle;160
12.2;A 2 Adiabatic Invariants;165
12.3;A 3 Non-linear Geometrical Optics;169
13;APPENDIX B: EVOLUTION OF ELECTRO-ACOUSTIC WAVES IN PLASMA WITH NEGATIVE DIELECTRIC PERMITTIVITY;171
13.1;B 1 Boundary Conditions;171
13.2;B 2 Excitation and Evolution of Electro-acoustic Waves;174
13.3;B 3 Solution of the Boundary-value Problem;183
13.4;B 4 General Solution of the Fundamental Equations;187
14;REFERENCES;190
15;INDEX;194
16;OTHER TITLES IN THE SERIES IN NATURAL PHILOSOPHY;198