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Non-linear waves in dispersive media

Author: Vladimir Iosifovich Karpman
Publisher: Oxford ; New York : Pergamon Press, [1974, ©1975]
Series: International series of monographs in natural philosophy, v. 71.
Edition/Format:   eBook : Document : English : [1st ed.]View all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Karpman, Vladimir Iosifovich.
Non-linear waves in dispersive media.
Oxford, New York, Pergamon Press, [1974, ©1975]
(DLC) 74004468
(OCoLC)841757
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Vladimir Iosifovich Karpman
ISBN: 9781483187150 1483187152
OCLC Number: 643580922
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL
Description: 1 online resource (xi, 186 pages) : illustrations.
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: Front Cover; Non-Linear Waves in Dispersive Media; Copyright Page; Table of Contents; PREFACE; INTRODUCTION; Chapter 1. LINEAR APPROXIMATION; 2 General Solution of the Linearized Equations; 3 Linearized Korteweg-de Vries Equation; Chapter 2. EXAMPLES OF DISPERSIVE MEDIA; 4 Gravitational Waves on Fluid Surfaces; 5 The Boussinesq Equation; 6 Ion-sound Waves in Unmagnetized Plasma; 7 Non-linear Waves in Magnetized Plasma; 8 Non-linear Electromagnetic Waves in Isotropie Dielectrics; 9 Sound Waves with Dispersion; Chapter 3. NON-LINEAR STATIONARY WAVES. 10 Steady Solutions of the Boussinesq Equations 11 Stationary Waves Propagating Transversely to the Magnetic Field in Rarefied Plasma (34-37, 3); 12 Other Examples of Stationary Waves; Chapter 4. NON-LINEAR WAVES IN WEAKLY DISPERSIVE MEDIA; 13 The Burgers Equation; 14 Solution of the Burgers Equation; 15 The Korteweg-de Vries Equation; 16 Conservation Laws for the Korteweg-de Vries Equation; 17 General Pattern of the Evolution of Initial Perturbations in Weakly Dispersive Media; 18 Analytical Solution of the Korteweg-de Vries Equation. 29 Self-focusing and Self-channelling of Waves 30 Electro-acoustic Waves in Plasma; APPENDIX A: NON-LINEAR WAVES WITH SLOWLY VARYING PARAMETERS (ADIABATIC APPROXIMATION OF WHITHAM); A 1 Variation Principle; A 2 Adiabatic Invariants; A 3 Non-linear Geometrical Optics; APPENDIX B: EVOLUTION OF ELECTRO-ACOUSTIC WAVES IN PLASMA WITH NEGATIVE DIELECTRIC PERMITTIVITY; B 1 Boundary Conditions; B 2 Excitation and Evolution of Electro-acoustic Waves; B 3 Solution of the Boundary-value Problem; B 4 General Solution of the Fundamental Equations; REFERENCES; INDEX.
Series Title: International series of monographs in natural philosophy, v. 71.
Responsibility: by V.I. Karpman ; translated by F.F. Cap. ; translation edited by S.M. Hamberger.

Abstract:

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 the.

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