Nonlinear Dispersive Waves And Fluids

Author : Avy Soffer
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 48,7 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 : Lokenath Debnath
Publisher : World Scientific
Page : 683 pages
File Size : 44,6 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 : Mark J. Ablowitz
Publisher : Cambridge University Press
Page : 363 pages
File Size : 44,7 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 : Marcelo Anile,P Pantano,G Russo,J Hunter
Publisher : CRC Press
Page : 255 pages
File Size : 52,8 Mb
Release : 2021-06-23
Category : Mathematics
ISBN : 9781000444858

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Ray Methods for Nonlinear Waves in Fluids and Plasmas by Marcelo Anile,P Pantano,G Russo,J Hunter Pdf

Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.

Author : Roger Grimshaw
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 41,6 Mb
Release : 2007-03-23
Category : Technology & Engineering
ISBN : 9783211380253

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Nonlinear Waves in Fluids: Recent Advances and Modern Applications by Roger Grimshaw Pdf

Although nonlinear waves occur in nearly all branches of physics and engi neering, there is an amazing degree of agreement about the fundamental con cepts and the basic paradigms. The underlying unity of the theory for linearized waves is already well-established, with the importance of such universal concepts as group velocity and wave superposition. For nonlinear waves the last few decades have seen the emergence of analogous unifying comcepts. The pervasiveness of the soliton concept is amply demonstrated by the ubiquity of such models as the Korteweg-de Vries equation and the nonlinear Schrodinger equation. Similarly, there is a universality in the study of wave-wave interactions, whether determin istic or statistical, and in the recent developments in the theory of wave-mean flow interactions. The aim of this text is to present the basic paradigms of weakly nonlinear waves in fluids. This book is the outcome of a CISM Summer School held at Udine from September 20-24, 2004. . Like the lectures given there the text covers asymptotic methods for the derivation of canonical evolution equations, such as the Kortew- de Vries and nonlinear Schrodinger equations, descriptions of the basic solution sets of these evolution equations, and the most relevant and compelling applica tions. These themes are interlocked, and this will be demonstrated throughout the text . The topics address any fluid flow application, but there is a bias towards geophysical fluid dynamics, reflecting for the most part the areas where many applications have been found.

Author : G. B. Whitham
Publisher : John Wiley & Sons
Page : 660 pages
File Size : 46,6 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 : David Henry
Publisher : Birkhäuser
Page : 0 pages
File Size : 48,8 Mb
Release : 2024-09-21
Category : Mathematics
ISBN : 3031635116

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Nonlinear Dispersive Waves by David Henry Pdf

This volume explores a number of exciting developments in the field of nonlinear dispersive waves with a particular focus on waves arising in the ocean. Chapters are based on talks given at the workshop “Nonlinear Dispersive Waves” that was held at University College Cork, Ireland, on April 24-25, 2023. Specific topics covered include: The recovery of steady rotational wave surface profiles; Hamiltonian models for the propagation of long gravity waves; Waves propagating at the surface of a fluid covered by floating ice plates; The use of spherical coordinates to describe arctic ocean waves; Boundary value problems related to the Muskat Problem. Nonlinear Dispersive Waves will appeal to researchers as well as graduate students interested in this active area of research.

Author : Miguel Onorato,Stefania Resitori,Fabio Baronio
Publisher : Springer
Page : 370 pages
File Size : 53,9 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 : Vladimir Evgenʹevich Zakharov
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 45,5 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 : Lokenath Debnath
Publisher : World Scientific Publishing Company Incorporated
Page : 669 pages
File Size : 52,8 Mb
Release : 1992-01-01
Category : Science
ISBN : 9810209487

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Nonlinear Dispersive Wave Systems by Lokenath Debnath Pdf

Author : A M Kamchatnov
Publisher : World Scientific
Page : 396 pages
File Size : 50,9 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 : B.K Shivamoggi
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400927728

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Introduction to Nonlinear Fluid-Plasma Waves by B.K Shivamoggi Pdf

A variety of nonlinear effects occur in a plasma. First, there are the wave steepening effects which can occur in any fluid in which the propagation speed depends upon the wave-amplitude. In a dispersive medium this can lead to classes of nonlinear waves which may have stationary solutions like solitons and shocks. Because the plasma also acts like an inherently nonlinear dielectric resonant interactions among waves lead to exchange of energy among them. Further, an electromagnetic wave interacting with a plasma may parametrically excite other waves in the plasma. A large-amplitude Langmuir wave undergoes a modulational instability which arises through local depressions in plasma density and the corresponding increases in the energy density of the wave electric field. Whereas a field collapse occurs in two and three dimensions, in a one-dimensional case, spatially localized stationary field structures called Langmuir solitons can result. Many other plasma waves like upper-hybrid waves, lower-hybrid waves etc. can also undergo a modulational instability and produce localized field structures. A new type of nonlinear effect comes into play when an electromagnetic wave propagating through a plasma is strong enough to drive the electrons to relativistic speeds. This leads to a propagation of an electromagnetic wave in a normally overdense plasma, and the coupling of the electromagnetic wave to a Langmuir wave in the plasma. The relativistic mass variation of the electrons moving in an intense electromagnetic wave can also lead to a modulational instability of the latter.

Author : Mitsuhiro Tanaka
Publisher : Springer Nature
Page : 237 pages
File Size : 54,7 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031026119

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Physics of Nonlinear Waves by Mitsuhiro Tanaka Pdf

This is an introductory book about nonlinear waves. It focuses on two properties that various different wave phenomena have in common, the "nonlinearity" and "dispersion", and explains them in a style that is easy to understand for first-time students. Both of these properties have important effects on wave phenomena. Nonlinearity, for example, makes the wave lean forward and leads to wave breaking, or enables waves with different wavenumber and frequency to interact with each other and exchange their energies. Dispersion, for example, sorts irregular waves containing various wavelengths into gentler wavetrains with almost uniform wavelengths as they propagate, or cause a difference between the propagation speeds of the wave waveform and the wave energy. Many phenomena are introduced and explained using water waves as an example, but this is just a tool to make it easier to draw physical images. Most of the phenomena introduced in this book are common to all nonlinear and dispersive waves. This book focuses on understanding the physical aspects of wave phenomena, and requires very little mathematical knowledge. The necessary minimum knowledges about Fourier analysis, perturbation method, dimensional analysis, the governing equations of water waves, etc. are provided in the text and appendices, so even second- or third-year undergraduate students will be able to fully understand the contents of the book and enjoy the fan of nonlinear wave phenomena without relying on other books.

Author : Sir M. J. Lighthill,James Lighthill
Publisher : Cambridge University Press
Page : 528 pages
File Size : 47,5 Mb
Release : 2001-11-15
Category : Mathematics
ISBN : 0521010454

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Waves in Fluids by Sir M. J. Lighthill,James Lighthill Pdf

A comprehensive textbook in which the author describes the science of waves in liquids and gases. Drawing on a subject of enormous extent and variety, he provides his readers with a thorough analysis of the most important and representative types of waves including sound waves, shock waves, waterwaves of all kinds, and the so-called internal waves (inside atmospheres and oceans) due to intensity stratification. Emphasis throughout is on the most generally useful fundamental ideas of wave science, including the principles of how waves interact with flows. This standard work on one of the great subdivisions of the dynamics of fluids is lucidly written and will be invaluable to engineers, physicists, geophysicists, applied mathematicians or any research worker concerned with wave motions or fluid fllows. It is especially suitable as a textbook for courses at the final year undergraduate or graduate level.

Author : P. L. Bhatnagar
Publisher : Oxford University Press, USA
Page : 162 pages
File Size : 47,7 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