Author: Michael P. Mortell
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
Book Description
A regular perturbation scheme is given for calculating small amplitude nonlinear periodic waves in a medium of finite extent. The first term in the asymptotic expansion is an arbitrary linear standing wave. The signal carried by the waves is determined from the nonlinear terms in the governing equations by an application of the Fredholm alternative. This gives a systematic scheme for calculating the corrections to the basic flow. The first problem considered is the resonant forced motion of a polytropic gas contained in a tube with its end closed. The second problem concerns the free vibration of an anharmonic lattice, or a nonlinear dispersive string. (Author).
Nonlinear Periodic Waves in a Bounded Medium: A Regular Perturbation Approach
Author: Michael P. Mortell
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
Book Description
A regular perturbation scheme is given for calculating small amplitude nonlinear periodic waves in a medium of finite extent. The first term in the asymptotic expansion is an arbitrary linear standing wave. The signal carried by the waves is determined from the nonlinear terms in the governing equations by an application of the Fredholm alternative. This gives a systematic scheme for calculating the corrections to the basic flow. The first problem considered is the resonant forced motion of a polytropic gas contained in a tube with its end closed. The second problem concerns the free vibration of an anharmonic lattice, or a nonlinear dispersive string. (Author).
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
Book Description
A regular perturbation scheme is given for calculating small amplitude nonlinear periodic waves in a medium of finite extent. The first term in the asymptotic expansion is an arbitrary linear standing wave. The signal carried by the waves is determined from the nonlinear terms in the governing equations by an application of the Fredholm alternative. This gives a systematic scheme for calculating the corrections to the basic flow. The first problem considered is the resonant forced motion of a polytropic gas contained in a tube with its end closed. The second problem concerns the free vibration of an anharmonic lattice, or a nonlinear dispersive string. (Author).
Scientific and Technical Aerospace Reports
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 538
Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 538
Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Nonlinear Periodic Waves And Their Modulations: An Introductory Course
Author: Anatoly M Kamchatnov
Publisher: World Scientific
ISBN: 9814492434
Category : Science
Languages : en
Pages : 399
Book Description
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.
Publisher: World Scientific
ISBN: 9814492434
Category : Science
Languages : en
Pages : 399
Book Description
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.
Nonlinear Waves In Bounded Media: The Mathematics Of Resonance
Author: Brian R Seymour
Publisher: World Scientific
ISBN: 9813100354
Category : Technology & Engineering
Languages : en
Pages : 420
Book Description
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.
Publisher: World Scientific
ISBN: 9813100354
Category : Technology & Engineering
Languages : en
Pages : 420
Book Description
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.
Bibliography of Scientific and Industrial Reports
Asymptotic Perturbation Theory Of Waves
Author: Lev Ostrovsky
Publisher: World Scientific
ISBN: 178326473X
Category : Juvenile Nonfiction
Languages : en
Pages : 227
Book Description
This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theoretical ideas are illustrated by many physical examples throughout the book.
Publisher: World Scientific
ISBN: 178326473X
Category : Juvenile Nonfiction
Languages : en
Pages : 227
Book Description
This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theoretical ideas are illustrated by many physical examples throughout the book.
Nuclear Science Abstracts
U.S. Government Research & Development Reports
Government Reports Announcements
Government Reports Index
Author:
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 1096
Book Description
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 1096
Book Description