Nonlinear Dispersive Waves

Author : Mark J. Ablowitz
Publisher : Cambridge University Press
Page : 363 pages
File Size : 48,5 Mb
Release : 2011-09-08
Category : Mathematics
ISBN : 9781139503488

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Nonlinear Dispersive Waves by Mark J. Ablowitz Pdf

The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.

Author : Herbert Koch,Daniel Tataru,Monica Vişan
Publisher : Springer
Page : 310 pages
File Size : 52,6 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 : G. B. Whitham
Publisher : John Wiley & Sons
Page : 660 pages
File Size : 43,5 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 : Lokenath Debnath
Publisher : World Scientific
Page : 683 pages
File Size : 49,5 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 : V. I. Karpman
Publisher : Elsevier
Page : 199 pages
File Size : 41,8 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 : P. L. Bhatnagar
Publisher : Oxford University Press, USA
Page : 162 pages
File Size : 43,9 Mb
Release : 1979
Category : Language Arts & Disciplines
ISBN : UOM:39015014360096

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Nonlinear Waves in One-dimensional Dispersive Systems by P. L. Bhatnagar Pdf

Author : A.I. Maimistov,A.M. Basharov
Publisher : Springer Science & Business Media
Page : 668 pages
File Size : 44,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401724487

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Nonlinear Optical Waves by A.I. Maimistov,A.M. Basharov Pdf

A non-linear wave is one of the fundamental objects of nature. They are inherent to aerodynamics and hydrodynamics, solid state physics and plasma physics, optics and field theory, chemistry reaction kinetics and population dynamics, nuclear physics and gravity. All non-linear waves can be divided into two parts: dispersive waves and dissipative ones. The history of investigation of these waves has been lasting about two centuries. In 1834 J. S. Russell discovered the extraordinary type of waves without the dispersive broadening. In 1965 N. J. Zabusky and M. D. Kruskal found that the Korteweg-de Vries equation has solutions of the solitary wave form. This solitary wave demonstrates the particle-like properties, i. e. , stability under propagation and the elastic interaction under collision of the solitary waves. These waves were named solitons. In succeeding years there has been a great deal of progress in understanding of soliton nature. Now solitons have become the primary components in many important problems of nonlinear wave dynamics. It should be noted that non-linear optics is the field, where all soliton features are exhibited to a great extent. This book had been designed as the tutorial to the theory of non-linear waves in optics. The first version was projected as the book covering all the problems in this field, both analytical and numerical methods, and results as well. However, it became evident in the process of work that this was not a real task.

Author : Muthusamy Lakshmanan,Shanmuganathan Rajaseekar
Publisher : Springer Science & Business Media
Page : 628 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642556883

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Nonlinear Dynamics by Muthusamy Lakshmanan,Shanmuganathan Rajaseekar Pdf

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Author : Lokenath Debnath
Publisher : World Scientific Publishing Company Incorporated
Page : 669 pages
File Size : 41,5 Mb
Release : 1992-01-01
Category : Science
ISBN : 9810209487

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Nonlinear Dispersive Wave Systems by Lokenath Debnath Pdf

Author : Avy Soffer
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 50,5 Mb
Release : 2019-03-12
Category : Nonlinear wave equations
ISBN : 9781470441098

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Nonlinear Dispersive Waves and Fluids by Avy Soffer Pdf

This volume contains the proceedings of the AMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations and the AMS Special Session on PDE Analysis on Fluid Flows, which were held in January 2017 in Atlanta, Georgia. These two sessions shared the underlying theme of the analysis aspect of evolutionary PDEs and mathematical physics. The articles address the latest trends and perspectives in the area of nonlinear dispersive equations and fluid flows. The topics mainly focus on using state-of-the-art methods and techniques to investigate problems of depth and richness arising in quantum mechanics, general relativity, and fluid dynamics.

Author : A M Kamchatnov
Publisher : World Scientific
Page : 396 pages
File Size : 51,5 Mb
Release : 2000-09-05
Category : Science
ISBN : 9789814492430

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Nonlinear Periodic Waves and Their Modulations by A M 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. Contents:Introduction and Basic ConceptsNonlinear Wave Equations in PhysicsWhitham Theory of ModulationsComplete Integrability of Nonlinear Wave EquationsPeriodic SolutionsDissipationless Shock WaveNonlinear Theory of Modulational InstabilityAppendices:Some Formulas from the Theory of Elliptic FunctionsAlgebraic Resolvents of Fourth Degree PolynomialsSolutions to Exercises Readership: Advanced graduate students and young researchers in nonlinear wave theory. Keywords:Nonlinear Waves;Solitons;Integrable Equations;Inverse Scattering Transform;Periodic Solutions;Whitham Theory;Modulation;Hodograph Transform;Dissipationless Shock Waves;Modulational Instability

Author : Lokenath Debnath
Publisher : CUP Archive
Page : 376 pages
File Size : 53,8 Mb
Release : 1983-12-30
Category : Mathematics
ISBN : 052125468X

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Nonlinear Waves by Lokenath Debnath Pdf

The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 50,5 Mb
Release : 2006
Category : Differential equations, Partial
ISBN : 9780821841433

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Nonlinear Dispersive Equations by Terence Tao Pdf

"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".

Author : Peter Janssen
Publisher : Cambridge University Press
Page : 310 pages
File Size : 48,8 Mb
Release : 2004-10-28
Category : Science
ISBN : 9780521465403

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The Interaction of Ocean Waves and Wind by Peter Janssen Pdf

This book was published in 2004. The Interaction of Ocean Waves and Wind describes in detail the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days. Winds generate ocean waves, but at the same time airflow is modified due to the loss of energy and momentum to the waves; thus, momentum loss from the atmosphere to the ocean depends on the state of the waves. This volume discusses ocean wave evolution according to the energy balance equation. An extensive overview of nonlinear transfer is given, and as a by-product the role of four-wave interactions in the generation of extreme events, such as freak waves, is discussed. Effects on ocean circulation are described. Coupled ocean-wave, atmosphere modelling gives improved weather and wave forecasts. This volume will interest ocean wave modellers, physicists and applied mathematicians, and engineers interested in shipping and coastal protection.

Author : Vladimir Evgenʹevich Zakharov
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 53,7 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.