Phase Shift for Strongly Nonlinear Slowly Varying Oscillators with Perturbations PDF Download
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Author: Richard Haberman
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
Author: Richard Haberman
Publisher:
ISBN:
Category :
Languages : en
Pages : 14
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Book Description
Author: F. J. Bourland
Publisher:
ISBN:
Category :
Languages : en
Pages : 84
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Book Description
The equations for the spatial and temporal modulations of the phase shift for slowly varying strongly nonlinear oscillators and dispersive waves have been determined for the first time. The effects of dissipative perturbations have been investigated for nonlinear oscillatory solutions of ordinary and partial differential equations (described by Klein-Gordon and Korteweg-de Vries type equations). The phase shift equations were derived using the method of multiple scales by evaluating the small perturbations to the exact action equation, a somewhat simpler technique than usual elimination of secular terms at an even higher order in the asymptotic expansion. It has been shown that, for dissipative perturbations, the frequency and action equations are valid to higher order and that their variations are only due to perturbations in the wave number and the averaged amplitude parameters. For second-order ordinary differential equations, the phase shift is determined from initial conditions in straight-forward manner since it was shown that there exists a new adiabatic invariant.
Author: F. Jay Bourland
Publisher:
ISBN:
Category : Wave-motion, Theory of
Languages : en
Pages : 34
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Book Description
Author: Lokenath Debnath
Publisher: World Scientific
ISBN: 9814554960
Category :
Languages : en
Pages : 683
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Book Description
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: Hans G. Kaper
Publisher: CRC Press
ISBN: 1482277069
Category : Mathematics
Languages : en
Pages : 283
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Book Description
Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
Author: F. J. Bourland
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Book Description
Author: J.K. Kevorkian
Publisher: Springer Science & Business Media
ISBN: 1461239680
Category : Mathematics
Languages : en
Pages : 642
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Book Description
This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.
Author: Paul K. Newton
Publisher: Springer Science & Business Media
ISBN: 146849290X
Category : Mathematics
Languages : en
Pages : 430
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Book Description
This text is an introduction to current research on the N- vortex problem of fluid mechanics. It describes the Hamiltonian aspects of vortex dynamics as an entry point into the rather large literature on the topic, with exercises at the end of each chapter.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 604
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Book Description
Author: Robert E. O'Malley
Publisher: Springer
ISBN: 3319119249
Category : Mathematics
Languages : en
Pages : 263
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Book Description
This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.
