Non Linear Waves In Dispersive Media

Author : V. I. Karpman
Publisher : Elsevier
Page : 199 pages
File Size : 46,8 Mb
Release : 2016-01-22
Category : Science
ISBN : 9781483187150

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Non-Linear Waves in Dispersive Media by V. I. Karpman 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.

Author : Vladimir Iosifovic Karpman
Publisher : Unknown
Page : 183 pages
File Size : 41,7 Mb
Release : 1975
Category : Nonlinear theories
ISBN : OCLC:488598685

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Non-linear Waves in Dispersive Media by Vladimir Iosifovic Karpman Pdf

Author : G. B. Whitham
Publisher : John Wiley & Sons
Page : 660 pages
File Size : 49,7 Mb
Release : 2011-10-18
Category : Science
ISBN : 9781118031209

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Linear and Nonlinear Waves by G. B. Whitham Pdf

Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.

Author : Herbert Koch,Daniel Tataru,Monica Vişan
Publisher : Springer
Page : 310 pages
File Size : 54,7 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9783034807364

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Dispersive Equations and Nonlinear Waves by Herbert Koch,Daniel Tataru,Monica Vişan Pdf

The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research.​

Author : Seymour Brian R,Mortell Michael P
Publisher : World Scientific
Page : 420 pages
File Size : 51,6 Mb
Release : 2017-01-18
Category : Technology & Engineering
ISBN : 9789813100350

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Nonlinear Waves In Bounded Media: The Mathematics Of Resonance by Seymour Brian R,Mortell Michael P Pdf

This unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent. It involves both standing (unforced) waves and resonant oscillations due to external periodic forcing. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media. The examples used come mainly from gas dynamics, water waves and viscoelastic waves.

Author : Vladimir Evgenʹevich Zakharov
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 54,8 Mb
Release : 1998
Category : Hamiltonian systems
ISBN : 0821841130

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Nonlinear Waves and Weak Turbulence by Vladimir Evgenʹevich Zakharov Pdf

This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincare normal forms and the inverse scattering method.

Author : Jüri Engelbrecht
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642747892

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Nonlinear Waves in Active Media by Jüri Engelbrecht Pdf

TIlis volume contains the contributions to the Euromech Colloquium No. 241 on Nonlinear Waves in Active Media at the Institute of Cybernetics of the Estonian Academy of Sciences, Tallinn, Estonia, USSR, September 27-30, 1988. The Co-chairmen of the Euromech Colloquium felt that it would be a good service to the community to publish these proceedings. First, the topic itself dealing with various wave processes with energy influx is extremely interesting and attracted a much larger number of participants than usual - a clear sign of its importance to the scientific community. Second, Euromech No. 241 was actually the first Euromech Colloquium held in the Soviet Union and could thus be viewed as a milestone in the extending scientific contacts between East and West. At the colloquium 50 researchers working in very different branches of sci ence met to lecture on their results and to discuss problems of common interest. An introductory paper by I. Engelbrecht presents the common motivation and background of the topics covered. Altogether 36 speakers presented their lectures, of which 30 are gathered here. The remaining six papers which will appear elsewhere are listed on page X. In addition, three contributions by authors who could not attend the colloquium are included. The two lectures given by A.S. Mikhailov, V.S. Davydov and V.S. Zykov are here published as one long paper.

Author : Miguel Onorato,Stefania Resitori,Fabio Baronio
Publisher : Springer
Page : 370 pages
File Size : 48,8 Mb
Release : 2016-09-19
Category : Science
ISBN : 9783319392141

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Rogue and Shock Waves in Nonlinear Dispersive Media by Miguel Onorato,Stefania Resitori,Fabio Baronio Pdf

This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.

Author : K. Naugolnykh,L. Ostrovsky
Publisher : Cambridge University Press
Page : 316 pages
File Size : 45,9 Mb
Release : 1998-05-28
Category : Mathematics
ISBN : 052139984X

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Nonlinear Wave Processes in Acoustics by K. Naugolnykh,L. Ostrovsky Pdf

This text considers models of different "acoustic" media as well as equations and behavior of finite-amplitude waves. It also considers the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction on the evolution and interaction of acoustic beams.

Author : Mikhail Viktorovich Kuzelev,Anri Amvrosievich Rukhadze
Publisher : World Scientific
Page : 271 pages
File Size : 49,7 Mb
Release : 2010
Category : Science
ISBN : 9789814261708

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Methods of Wave Theory in Dispersive Media by Mikhail Viktorovich Kuzelev,Anri Amvrosievich Rukhadze Pdf

Ch. 1. Linear harmonic waves in dispersive systems. Initial-value problem and problem with an external source. 1. Harmonic waves in dispersive systems. 2. Initial-value problem. Eigenmode method. 3. Characteristic function of the state vector. Dispersion operator. 4. Laplace transform method -- ch. 2. A case study of linear waves in dispersive media. 5. Transverse electromagnetic waves in an isotropic dielectric. 6. Longitudinal electrostatic waves in a cold isotropic plasma. Collisional dissipation of plasma waves. 7. Transverse electromagnetic waves in a cold isotropic plasma. Dissipation of transverse waves in a plasma. 8. Electromagnetic waves in metals. 9. Electromagnetic waves in a waveguide with an isotropic dielectric. 10. Longitudinal waves in a hot isotropic plasma. Electron diffusion in a plasma. 11. Longitudinal waves in an isotropic degenerate plasma. Waves in a quantum plasma. 12. Ion acoustic waves in a nonisothermal plasma. Ambipolar diffusion. 13. Electromagnetic waves in a waveguide with an anisotropic plasma in a strong external magnetic field. 14. Electromagnetic waves propagating in a magnetized electron plasma along a magnetic field. 15. Electrostatic waves propagating in a magnetized electron plasma at an angle to a magnetic field. 16. Magnetohydrodynamic waves in a conducting fluid. 17. Acoustic waves in crystals. 18. Longitudinal electrostatic waves in a one-dimensional electron beam. 19. Beam instability in a plasma. 20. Instability of a current-carrying plasma -- ch. 3. Linear waves in coupled media. Slow amplitude method. 21. Coupled oscillator representation and slow amplitude method. 22. Beam-plasma system in the coupled oscillator representation. 23. Basic equations of microwave electronics. 24. Resonant Buneman instability in a current-carrying plasma in the coupled oscillator representation. 25. Dispersion function and wave absorption in dissipative systems. 26. Some effects in the interaction between waves in coupled systems. 27. Waves and their interaction in periodic structures -- ch. 4. Nonharmonic waves in dispersive media. 28. General solution to the initial-value problem. 29. Quasi-harmonic approximation. Group velocity. 30. Pulse spreading in equilibrium dispersive media. 31. Stationary-phase method. 32. Some problems for wave equations with a source -- ch. 5. Nonharmonic waves in nonequilibrium media. 33. Pulse propagation in nonequilibrium media. 34. Stationary-phase method for complex frequencies. 35. Quasi-harmonic approximation in the theory of interaction of electron beams with slowing-down media -- ch. 6. Theory of instabilities. 36. Convective and absolute instabilities. First criterion for the type of instability. 37. Saddle-point method. Second criterion for the type of instability. 38. Third Criterion for the type of instability. 39. Type of beam instability in the interaction with a slowed wave of zero group velocity in a medium. 40. Calculation of the Green's functions of unstable systems -- ch. 7. Hamiltonian method in the theory of electromagnetic radiation in dispersive media. 41. Equations for the excitation of transverse electromagnetic field oscillators. 42. Dipole radiation. 43. Radiation from a moving dipole - undulator radiation. 44. Cyclotron radiation. 45. Cherenkov effect. Anomalous and normal doppler effects. 46. Application of the Hamiltonian method to the problem of the excitation of longitudinal waves

Author : Anatoli? Mikha?lovich Kamchatnov
Publisher : World Scientific
Page : 399 pages
File Size : 50,9 Mb
Release : 2000
Category : Science
ISBN : 9789810244071

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Nonlinear Periodic Waves and Their Modulations by Anatoli? Mikha?lovich Kamchatnov Pdf

Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions.

Author : С. Н Гурбатов,А. Н Малахов,А. И Саичев
Publisher : Manchester University Press
Page : 334 pages
File Size : 52,6 Mb
Release : 1991
Category : Nonlinear theories
ISBN : 071903275X

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Nonlinear Random Waves and Turbulence in Nondispersive Media by С. Н Гурбатов,А. Н Малахов,А. И Саичев Pdf

Author : Lokenath Debnath
Publisher : World Scientific
Page : 683 pages
File Size : 49,8 Mb
Release : 1992-09-09
Category : Electronic
ISBN : 9789814554961

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Nonlinear Dispersive Wave Systems by Lokenath Debnath Pdf

This book brings together a comprehensive account of major developments in the theory and applications of nonlinear dispersive waves, nonlinear water waves, KdV and nonlinear Schrodinger equations, Davey-Stewartson equation, Benjamin-Ono equation and nonlinear instability phenomena. In order to give the book a wider readership, chapters have been written by internationally known researchers who have made significant contributions to nonlinear waves and nonlinear instability. This volume will be invaluable to applied mathematicians, physicists, geophysicists, oceanographers, engineering scientists, and to anyone interested in nonlinear dynamics.

Author : Vasily Y. Belashov,Sergey V. Vladimirov
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 40,8 Mb
Release : 2006-01-20
Category : Science
ISBN : 9783540268802

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Solitary Waves in Dispersive Complex Media by Vasily Y. Belashov,Sergey V. Vladimirov Pdf

Deals with the theoretical, analytical and advanced numerical study of the structure and dynamics of one-dimensional as well as two- and three-dimensional solitons and nonlinear waves described by Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP), nonlinear Schrodinger (NLS) and derivative NLS (DNLS) classes of equations.

Author : Gérard A. Maugin
Publisher : Unknown
Page : 328 pages
File Size : 50,6 Mb
Release : 1999
Category : Mathematics
ISBN : 0198534841

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Nonlinear Waves in Elastic Crystals by Gérard A. Maugin Pdf

The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. Students are introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.