Linear And Nonlinear Waves

Author: G. B. Whitham
Editor: John Wiley & Sons
ISBN: 1118031202
File Size: 43,54 MB
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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.

Linear And Nonlinear Waves In Microstructured Solids

Author: Igor V. Andrianov
Editor: CRC Press
ISBN: 1000372219
File Size: 70,56 MB
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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.

Linear And Nonlinear Waves

Author: G. B. Whitham
Editor: Wiley-Interscience
ISBN:
File Size: 52,44 MB
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This work is an account of the underlying mathematical theory with emphasis on the unifying ideas and the main points that illuminate the behaviour of waves. The book is divided into two parts, hyperbolic waves and dispersive waves.

Linear And Nonlinear Waves

Author: G. B. Whitham
Editor: Wiley-Interscience
ISBN:
File Size: 12,77 MB
Format: PDF, Kindle
Read: 1528
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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.

Linear And Nonlinear Wave Propagation

Author: Spencer P Kuo
Editor:
ISBN: 9789811231636
File Size: 50,74 MB
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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 Waves Classical And Quantum Aspects

Author: Fatkhulla Abdullaev
Editor: Springer Science & Business Media
ISBN: 1402021909
File Size: 34,76 MB
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Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices (including quantum and nonlinear lattices), and nonlinear optics and photonics. Classical and quantum aspects of the dynamics of nonlinear waves are considered. The contributions focus on the Gross-Pitaevskii equation and on the quantum nonlinear Schrödinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.

Advances In Nonlinear Waves And Symbolic Computation

Author: Zhenya Yan
Editor: Nova Science Pub Incorporated
ISBN:
File Size: 30,90 MB
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With the rapid development of science and technology, the computer has become an important tool in many science fields. Particularly, symbolic computation, which is one of the most exciting and challenging areas. It has been applied in many sciences such as mathematics, physics, chemistry, biology, mechanics, engineering, etc., in particular, non-linear sciences ad complex sciences. Nowadays, many symbolic computation softwares have been used to deal with these problems. Up to now, there have existed many non-linear differential/difference systems related to solitons and chaos in the non-linear science field. In order to understand these complex physical phenomena, it is important to research some of their basic properties. Because of the complexity of these non-linear systems, with the symbolic computation, this new book presents important research on non-linear differential/difference systems, related to solitons and chaos as well as other non-linear sciences in views of constructive algorithms.

Linear And Nonlinear Spin Waves In Magnetic Films And Superlattices

Author: Michael G. Cottam
Editor: World Scientific
ISBN: 9789810210069
File Size: 44,77 MB
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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.

Lectures On Non Linear Wave Equations

Author: Christopher Donald Sogge
Editor: International Pressof Boston Incorporated
ISBN:
File Size: 60,65 MB
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Presents an account of the basic facts concerning the linear wave equation and the methods from harmonic analysis that are necessary when studying nonlinear hyperbolic differential equations. This book examines quasilinear equations with small data where the Klainerman-Sobolev inequalities and weighted space-time estimates are introduced.

Nonlinear Waves Solitons And Chaos

Author: Eryk Infeld
Editor: Cambridge University Press
ISBN: 9780521635578
File Size: 71,85 MB
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This revised and updated second edition of a highly successful book is the only text at this level to embrace a universal approach to three major developments in classical physics; namely nonlinear waves, solitons and chaos. The authors now include new material on biology and laser theory, and go on to discuss important recent developments such as soliton metamorphosis. A comprehensive treatment of basic plasma and fluid configurations and instabilities is followed by a study of the relevant nonlinear structures. Each chapter concludes with a set of problems. This text will be particularly valuable for students taking courses in nonlinear aspects of physics. In general, it will be of value to final year undergraduates and beginning graduate students studying fluid dynamics, plasma physics and applied mathematics.

Nonlinear Waves And Offshore Structures

Author: Cheung Hun Kim
Editor: World Scientific
ISBN: 9810248849
File Size: 64,68 MB
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The responses of offshore structures are significantly affected by steep nonlinear waves, currents and wind, leading to phenomena such as springing and ringing of TLPs, slow drift yaw motion of FPSOs and large oscillations of Spar platforms due to vortex shedding. Research has brought about significant progress in this field over the past few decades and introduced us to increasingly involved concepts and their diverse applicability. Thus, an in-depth understanding of steep nonlinear waves and their effects on the responses of offshore structures is essential for safe and effective designs.This book deals with analyses of nonlinear problems encountered in the design of offshore structures, as well as those that are of immediate practical interest to ocean engineers and designers. It presents conclusions drawn from recent research pertinent to nonlinear waves and their effects on the responses of offshore structures. Theories, observations and analyses of laboratory and field experiments are expounded such that the nonlinear effects can be clearly visualized.

Nonlinear Waves

Author: Lokenath Debnath
Editor: CUP Archive
ISBN: 9780521254687
File Size: 27,33 MB
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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.

Wave Propagation In Linear And Nonlinear Periodic Media

Author: Francesco Romeo
Editor: Springer Science & Business Media
ISBN: 3709113091
File Size: 65,28 MB
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Waves and defect modes in structures media.- Piezoelectric superlattices and shunted periodic arrays as tunable periodic structures and metamaterials.- Topology optimization.- Map-based approaches for periodic structures.- Methodologies for nonlinear periodic media.​ The contributions in this volume present both the theoretical background and an overview of the state-of-the art in wave propagation in linear and nonlinear periodic media in a consistent format. They combine the material issued from a variety of engineering applications, spanning a wide range of length scale, characterized by structures and materials, both man-made and naturally occurring, featuring geometry, micro-structural and/or materials properties that vary periodically in space, including periodically stiffened plates, shells and beam-like as well as bladed disc assemblies, phononic metamaterials, photonic crystals and ordered granular media. Along with linear models and applications, analytical methodologies for analyzing and exploiting complex dynamical phenomena arising in nonlinear periodic systems are also presented.​

Oscillations And Waves

Author: M.I Rabinovich
Editor: Springer Science & Business Media
ISBN: 9400910339
File Size: 13,23 MB
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'Et mai - ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y semis point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost sheJf next to the dusty canister Iabclled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Nonlinear Wave Processes In Acoustics

Author: K. Naugolnykh
Editor: Cambridge University Press
ISBN: 9780521399845
File Size: 64,93 MB
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This text considers models of different "acoustic" media as well as equations and behavior of finite-amplitude waves. It also considers the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction on the evolution and interaction of acoustic beams.

Nonlinear Waves In One Dimensional Dispersive Systems

Author: P. L. Bhatnagar
Editor: Oxford University Press, USA
ISBN:
File Size: 51,41 MB
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Introduction To Wave Propagation In Nonlinear Fluids And Solids

Author: D. S. Drumheller
Editor: Cambridge University Press
ISBN: 9780521587464
File Size: 16,36 MB
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Waves occur widely in nature and have innumerable commercial uses. Pressure waves are responsible for the transmission of speech, bow waves created by meteors can virtually ignite the earth's atmosphere, ultrasonic waves are used for medical imaging, and shock waves are used for the synthesis of new materials. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models. It covers gases, liquids, and solids as integral parts of the subject. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Graduate students, as well as professional engineers and applied physicists, will value this clear, comprehensive introduction to the study of wave phenomena.

Waves In Nonlinear Pre Stressed Materials

Author: M. Destrade
Editor: Springer Science & Business Media
ISBN: 3211735720
File Size: 43,67 MB
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Papers in this book provide a state-of-the-art examination of waves in pre-stressed materials. You’ll gain new perspectives via a multi-disciplinary approach that interweaves key topics. These topics include the mathematical modeling of incremental material response (elastic and inelastic), an analysis of the governing differential equations, and boundary-value problems. Detailed illustrations help you visualize key concepts and processes.

Nonlinear Wave Equations

Author: Walter A. Strauss
Editor: American Mathematical Soc.
ISBN: 0821807250
File Size: 10,24 MB
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The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.

Nonlinear Waves In Networks

Author: Felix Ali Mehmeti
Editor: De Gruyter Akademie Forschung
ISBN:
File Size: 42,33 MB
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Philosophy, economics, and politics are the three most important coordinates that define the work of Karl Marx. The texts collected in this volume undertake a systematic reflection of these three realms and their inter-relationships in the context of contemporary social and political change. They offer an overview of the breadth of modern methods and ways of thinking that are related to Marx.