Linear And Nonlinear Wave Propagation

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Linear And Nonlinear Waves

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Author : G. B. Whitham
language : en
Publisher: Wiley-Interscience
Release Date : 1999-07

Linear And Nonlinear Waves written by G. B. Whitham and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07 with Mathematics categories.

A Wiley-Interscience Series of Tests, Monographs, and Tracts.

Linear And Nonlinear Wave Propagation

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Author : Spencer P Kuo
language : en
Publisher: World Scientific
Release Date : 2021-04-16

Linear And Nonlinear Wave Propagation written by Spencer P Kuo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-16 with Science categories.

Waves are essential phenomena in most scientific and engineering disciplines, such as electromagnetism and optics, and different mechanics including fluid, solid, structural, quantum, etc. They appear in linear and nonlinear systems. Some can be observed directly and others are not. The features of the waves are usually described by solutions to either linear or nonlinear partial differential equations, which are fundamental to the students and researchers.Generic equations, describing wave and pulse propagation in linear and nonlinear systems, are introduced and analyzed as initial/boundary value problems. These systems cover the general properties of non-dispersive and dispersive, uniform and non-uniform, with/without dissipations. Methods of analyses are introduced and illustrated with analytical solutions. Wave-wave and wave-particle interactions ascribed to the nonlinearity of media (such as plasma) are discussed in the final chapter.This interdisciplinary textbook is essential reading for anyone in above mentioned disciplines. It was prepared to provide students with an understanding of waves and methods of solving wave propagation problems. The presentation is self-contained and should be read without difficulty by those who have adequate preparation in classic mechanics. The selection of topics and the focus given to each provide essential materials for a lecturer to cover the bases in a linear/nonlinear wave course.

Nonlinear Dispersive Waves

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Author : Mark J. Ablowitz
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-08

Nonlinear Dispersive Waves written by Mark J. Ablowitz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-08 with Mathematics categories.

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.

Nonlinear Waves In Integrable And Non Integrable Systems

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Author : Jianke Yang
language : en
Publisher: SIAM
Release Date : 2010-12-02

Nonlinear Waves In Integrable And Non Integrable Systems written by Jianke Yang and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-02 with Science categories.

Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).

A Course On Nonlinear Waves

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Author : S.S. Shen
language : en
Publisher: Springer
Release Date : 1993-06-30

A Course On Nonlinear Waves written by S.S. Shen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-30 with Mathematics categories.

The aim of this book is to give a self-contained introduction to the mathe matical analysis and physical explanations of some basic nonlinear wave phe nomena. This volume grew out of lecture notes for graduate courf;!es which I gave at the University of Alberta, the University of Saskatchewan, ·and Texas A&M University. As an introduction it is not intended to be exhaustive iQ its choice of material, but rather to convey to interested readers a basic; yet practical, methodology as well as some of the more important results obtained since the 1950's. Although the primary purpose of this volume is to serve as a textbook, it should be useful to anyone who wishes to understand or conduct research into nonlinear waves. Here, for the first time, materials on X-ray crystallography and the forced Korteweg-de Vries equation are incorporated naturally into a textbook on non linear waves. Another characteristic feature of the book is the inclusion of four symbolic calculation programs written in MATHEMATICA. They emphasize outcomes rather than numerical methods and provide certain symbolic and nu merical results related to solitons. Requiring only one or two commands to run, these programs have user-friendly interfaces. For example, to get the explicit expression of the 2-soliton of the Korteweg-de Vries equation, one only needs to type in soliton[2] when using the program solipac.m.

Wave Propagation In Electromagnetic Media

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Author : Julian L. Davis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Wave Propagation In Electromagnetic Media written by Julian L. Davis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

This is the second work of a set of two volumes on the phenomena of wave propagation in nonreacting and reacting media. The first, entitled Wave Propagation in Solids and Fluids (published by Springer-Verlag in 1988), deals with wave phenomena in nonreacting media (solids and fluids). This book is concerned with wave propagation in reacting media-specifically, in electro magnetic materials. Since these volumes were designed to be relatively self contained, we have taken the liberty of adapting some of the pertinent material, especially in the theory of hyperbolic partial differential equations (concerned with electromagnetic wave propagation), variational methods, and Hamilton-Jacobi theory, to the phenomena of electromagnetic waves. The purpose of this volume is similar to that of the first, except that here we are dealing with electromagnetic waves. We attempt to present a clear and systematic account of the mathematical methods of wave phenomena in electromagnetic materials that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical tech niques, and on showing how these methods of mathematical physics can be effective in unifying the physics of wave propagation in electromagnetic media. Chapter 1 presents the theory of time-varying electromagnetic fields, which involves a discussion of Faraday's laws, Maxwell's equations, and their appli cations to electromagnetic wave propagation under a variety of conditions.

Effective Computational Methods For Wave Propagation

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Author : Nikolaos A. Kampanis
language : en
Publisher: CRC Press
Release Date : 2008-02-25

Effective Computational Methods For Wave Propagation written by Nikolaos A. Kampanis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-25 with Mathematics categories.

Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable

Linear And Nonlinear Spin Waves In Magnetic Films And Superlattices

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Author : Michael G. Cottam
language : en
Publisher: World Scientific
Release Date : 1994

Linear And Nonlinear Spin Waves In Magnetic Films And Superlattices written by Michael G. Cottam and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.

In the past few years, there has been a rapidly growing interest in the properties of spin waves (or magnons) in ordered magnetic materials. These are the low-lying excitations that characterize the dynamical behavior of the magnetization variables in ferromagnets, ferrimagnets and antiferromagnets, particularly at low temperatures. Many of the recent developments concerning spin waves have been directed towards understanding their behavior in limited magnetic samples. At the same time, there have been dramatic advances in the experimental techniques, both for preparing high-quality magnetic samples in the form of thin films and superlattices and for the study of the spin-wave excitations themselves. Magnetic thin films have long been of technological as well as scientific interest and an understanding of both the linear and nonlinear aspects of their magnetic behavior is important.

Linear And Nonlinear Waves In Microstructured Solids

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Author : Igor V. Andrianov
language : en
Publisher: CRC Press
Release Date : 2021-04-22

Linear And Nonlinear Waves In Microstructured Solids written by Igor V. Andrianov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-22 with Technology & Engineering categories.

This book uses asymptotic methods to obtain simple approximate analytic solutions to various problems within mechanics, notably wave processes in heterogeneous materials. Presenting original solutions to common issues within mechanics, this book builds upon years of research to demonstrate the benefits of implementing asymptotic techniques within mechanical engineering and material science. Focusing on linear and nonlinear wave phenomena in complex micro-structured solids, the book determines their global characteristics through analysis of their internal structure, using homogenization and asymptotic procedures, in line with the latest thinking within the field. The book’s cutting-edge methodology can be applied to optimal design, non-destructive control and in deep seismic sounding, providing a valuable alternative to widely used numerical methods. Using case studies, the book covers topics such as elastic waves in nonhomogeneous materials, regular and chaotic dynamics based on continualisation and discretization and vibration localization in 1D Linear and Nonlinear lattices. The book will be of interest to students, research engineers, and professionals specialising in mathematics and physics as well as mechanical and civil engineering.

Nonlinear Dynamics

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Author : Muthusamy Lakshmanan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nonlinear Dynamics written by Muthusamy Lakshmanan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Integrability, chaos and patterns are three of the most important concepts in nonlinear dynamics. These are covered in this book from fundamentals to recent developments. The book presents a self-contained treatment of the subject to suit the needs of students, teachers and researchers in physics, mathematics, engineering and applied sciences who wish to gain a broad knowledge of nonlinear dynamics. It describes fundamental concepts, theoretical procedures, experimental and numerical techniques and technological applications of nonlinear dynamics. Numerous examples and problems are included to facilitate the understanding of the concepts and procedures described. In addition to 16 chapters of main material, the book contains 10 appendices which present in-depth mathematical formulations involved in the analysis of various nonlinear systems.