Mathematical Studies In Nonlinear Wave Propagation

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Mathematical Studies in Nonlinear Wave Propagation

Regional Research Conference on Mathematical Methods in Nonlinear Wave Propagation
Mathematical Studies in Nonlinear Wave Propagation Book PDF

Author : Regional Research Conference on Mathematical Methods in Nonlinear Wave Propagation
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 47,9 Mb
Release : 2005
Category : Nonlinear theories
ISBN : 9780821833490

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Mathematical Studies in Nonlinear Wave Propagation by Regional Research Conference on Mathematical Methods in Nonlinear Wave Propagation Pdf

Lively discussions and stimulating research were part of a five-day conference on Mathematical Methods in Nonlinear Wave Propagation sponsored by the NSF and CBMS. This volume is a collection of lectures and papers stemming from that event. Leading experts present dynamical systems and chaos, scattering and spectral theory, nonlinear wave equations, optimal control, optical waveguide design, and numerical simulation. The book is suitable for a diverse audience of mathematical specialists interested in fiber optic communications and other nonlinear phenomena. It is also suitable for engineers and other scientists interested in the mathematics of nonlinear wave propagation.

Nonlinear Wave Equations

Satyanad Kichenassamy
Nonlinear Wave Equations Book PDF

Author : Satyanad Kichenassamy
Publisher : CRC Press
Page : 297 pages
File Size : 50,6 Mb
Release : 2021-05-30
Category : Mathematics
ISBN : 9781000444728

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Nonlinear Wave Equations by Satyanad Kichenassamy Pdf

This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.

Nonlinear Wave Equations

Walter A. Strauss
Nonlinear Wave Equations Book PDF

Author : Walter A. Strauss
Publisher : American Mathematical Soc.
Page : 91 pages
File Size : 47,5 Mb
Release : 1990-01-12
Category : Mathematics
ISBN : 9780821807255

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Nonlinear Wave Equations by Walter A. Strauss Pdf

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.

Recent Mathematical Methods in Nonlinear Wave Propagation

Guy Boillat,Constantin M. Dafermos,Peter D. Lax,Tai-Ping Liu
Recent Mathematical Methods in Nonlinear Wave Propagation Book PDF

Author : Guy Boillat,Constantin M. Dafermos,Peter D. Lax,Tai-Ping Liu
Publisher : Springer
Page : 149 pages
File Size : 41,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540495659

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Recent Mathematical Methods in Nonlinear Wave Propagation by Guy Boillat,Constantin M. Dafermos,Peter D. Lax,Tai-Ping Liu Pdf

These lecture notes of the courses presented at the first CIME session 1994 by leading scientists present the state of the art in recent mathematical methods in Nonlinear Wave Propagation.

Nonlinear Wave Dynamics

J. Engelbrecht
Nonlinear Wave Dynamics Book PDF

Author : J. Engelbrecht
Publisher : Springer Science & Business Media
Page : 197 pages
File Size : 42,9 Mb
Release : 2013-04-17
Category : Technology & Engineering
ISBN : 9789401588911

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Nonlinear Wave Dynamics by J. Engelbrecht Pdf

At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.

Non-Linear Wave Propagation With Applications to Physics and Magnetohydrodynamics by A Jeffrey and T Taniuti

Anonim
Non Linear Wave Propagation With Applications to Physics and Magnetohydrodynamics by A Jeffrey and T Taniuti Book PDF

Author : Anonim
Publisher : Elsevier
Page : 322 pages
File Size : 50,9 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080957803

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Non-Linear Wave Propagation With Applications to Physics and Magnetohydrodynamics by A Jeffrey and T Taniuti by Anonim Pdf

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Applied Wave Mathematics II

Arkadi Berezovski,Tarmo Soomere
Applied Wave Mathematics II Book PDF

Author : Arkadi Berezovski,Tarmo Soomere
Publisher : Springer Nature
Page : 376 pages
File Size : 53,7 Mb
Release : 2019-11-16
Category : Mathematics
ISBN : 9783030299514

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Applied Wave Mathematics II by Arkadi Berezovski,Tarmo Soomere Pdf

This book gathers contributions on various aspects of the theory and applications of linear and nonlinear waves and associated phenomena, as well as approaches developed in a global partnership of researchers with the national Centre of Excellence in Nonlinear Studies (CENS) at the Department of Cybernetics of Tallinn University of Technology in Estonia. The papers chiefly focus on the role of mathematics in the analysis of wave phenomena. They highlight the complexity of related topics concerning wave generation, propagation, transformation and impact in solids, gases, fluids and human tissues, while also sharing insights into selected mathematical methods for the analytical and numerical treatment of complex phenomena. In addition, the contributions derive advanced mathematical models, share innovative ideas on computing, and present novel applications for a number of research fields where both linear and nonlinear wave problems play an important role. The papers are written in a tutorial style, intended for non-specialist researchers and students. The authors first describe the basics of a problem that is currently of interest in the scientific community, discuss the state of the art in related research, and then share their own experiences in tackling the problem. Each chapter highlights the importance of applied mathematics for central issues in the study of waves and associated complex phenomena in different media. The topics range from basic principles of wave mechanics up to the mathematics of Planet Earth in the broadest sense, including contemporary challenges in the mathematics of society. In turn, the areas of application range from classic ocean wave mathematics to material science, and to human nerves and tissues. All contributions describe the approaches in a straightforward manner, making them ideal material for educational purposes, e.g. for courses, master class lectures, or seminar presentations.

Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis

Adrian Constantin
Nonlinear Water Waves with Applications to Wave Current Interactions and Tsunamis Book PDF

Author : Adrian Constantin
Publisher : SIAM
Page : 333 pages
File Size : 50,7 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 161197187X

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Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis by Adrian Constantin Pdf

This overview of some of the main results and recent developments in nonlinear water waves presents fundamental aspects of the field and discusses several important topics of current research interest. It contains selected information about water-wave motion for which advanced mathematical study can be pursued, enabling readers to derive conclusions that explain observed phenomena to the greatest extent possible. The author discusses the underlying physical factors of such waves and explores the physical relevance of the mathematical results that are presented. The material is an expanded version of the author's lectures delivered at the NSF-CBMS Regional Research Conference in the Mathematical Sciences organized by the Mathematics Department of the University of Texas-Pan American in 2010.

Nonlinear Waves and Weak Turbulence

Vladimir Evgenʹevich Zakharov
Nonlinear Waves and Weak Turbulence Book PDF

Author : Vladimir Evgenʹevich Zakharov
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 49,8 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.

Nonlinear Waves

Lokenath Debnath
Nonlinear Waves Book PDF

Author : Lokenath Debnath
Publisher : CUP Archive
Page : 376 pages
File Size : 47,7 Mb
Release : 1983-12-30
Category : Mathematics
ISBN : 052125468X

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Nonlinear Waves by Lokenath Debnath Pdf

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.

Mathematics of Wave Propagation

Julian L. Davis
Mathematics of Wave Propagation Book PDF

Author : Julian L. Davis
Publisher : Princeton University Press
Page : 411 pages
File Size : 44,7 Mb
Release : 2021-01-12
Category : Mathematics
ISBN : 9780691223377

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Mathematics of Wave Propagation by Julian L. Davis Pdf

Earthquakes, a plucked string, ocean waves crashing on the beach, the sound waves that allow us to recognize known voices. Waves are everywhere, and the propagation and classical properties of these apparently disparate phenomena can be described by the same mathematical methods: variational calculus, characteristics theory, and caustics. Taking a medium-by-medium approach, Julian Davis explains the mathematics needed to understand wave propagation in inviscid and viscous fluids, elastic solids, viscoelastic solids, and thermoelastic media, including hyperbolic partial differential equations and characteristics theory, which makes possible geometric solutions to nonlinear wave problems. The result is a clear and unified treatment of wave propagation that makes a diverse body of mathematics accessible to engineers, physicists, and applied mathematicians engaged in research on elasticity, aerodynamics, and fluid mechanics. This book will particularly appeal to those working across specializations and those who seek the truly interdisciplinary understanding necessary to fully grasp waves and their behavior. By proceeding from concrete phenomena (e.g., the Doppler effect, the motion of sinusoidal waves, energy dissipation in viscous fluids, thermal stress) rather than abstract mathematical principles, Davis also creates a one-stop reference that will be prized by students of continuum mechanics and by mathematicians needing information on the physics of waves.

Selected Topics in Nonlinear Wave Mechanics

C.I. Christov,Arde Guran
Selected Topics in Nonlinear Wave Mechanics Book PDF

Author : C.I. Christov,Arde Guran
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200956

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Selected Topics in Nonlinear Wave Mechanics by C.I. Christov,Arde Guran Pdf

This book gives an overview ofthe current state of nonlinear wave mechanics with emphasis on strong discontinuities (shock waves) and localized self preserving shapes (solitons) in both elastic and fluid media. The exposition is intentionallyat a detailed mathematical and physical level, our expectation being that the reader will enjoy coming to grips in a concrete manner with advances in this fascinating subject. Historically, modern research in nonlinear wave mechanics began with the famous 1858 piston problem paper of Riemann on shock waves and con tinued into the early part of the last century with the work of Hadamard, Rankine, and Hugoniot. After WWII, research into nonlinear propagation of dispersive waves rapidly accelerated with the advent of computers. Works of particular importance in the immediate post-war years include those of von Neumann, Fermi, and Lax. Later, additional contributions were made by Lighthill, Glimm, Strauss, Wendroff, and Bishop. Dispersion alone leads to shock fronts of the propagating waves. That the nonlinearity can com pensate for the dispersion, leading to propagation with a stable wave having constant velocity and shape (solitons) came as a surprise. A solitary wave was first discussed by J. Scott Russell in 1845 in "Report of British Asso ciations for the Advancement of Science. " He had, while horseback riding, observed a solitary wave travelling along a water channel and followed its unbroken progress for over a mile.

Nonlinear Water Waves

David Henry,Konstantinos Kalimeris,Emilian I. Părău,Jean-Marc Vanden-Broeck,Erik Wahlén
Nonlinear Water Waves Book PDF

Author : David Henry,Konstantinos Kalimeris,Emilian I. Părău,Jean-Marc Vanden-Broeck,Erik Wahlén
Publisher : Springer Nature
Page : 218 pages
File Size : 53,9 Mb
Release : 2019-11-27
Category : Mathematics
ISBN : 9783030335366

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Nonlinear Water Waves by David Henry,Konstantinos Kalimeris,Emilian I. Părău,Jean-Marc Vanden-Broeck,Erik Wahlén Pdf

The motion of water is governed by a set of mathematical equations which are extremely complicated and intractable. This is not surprising when one considers the highly diverse and intricate physical phenomena which may be exhibited by a given body of water. Recent mathematical advances have enabled researchers to make major progress in this field, reflected in the topics featured in this volume. Cutting-edge techniques and tools from mathematical analysis have generated strong rigorous results concerning the qualitative and quantitative physical properties of solutions of the governing equations. Furthermore, accurate numerical computations of fully-nonlinear steady and unsteady water waves in two and three dimensions have contributed to the discovery of new types of waves. Model equations have been derived in the long-wave and modulational regime using Hamiltonian formulations and solved numerically. This book brings together interdisciplinary researchers working in the field of nonlinear water waves, whose contributions range from survey articles to new research results which address a variety of aspects in nonlinear water waves. It is motivated by a workshop which was organised at the Erwin Schrödinger International Institute for Mathematics and Physics in Vienna, November 27-December 7, 2017. The key aim of the workshop was to describe, and foster, new approaches to research in this field. This is reflected in the contents of this book, which is aimed to stimulate both experienced researchers and students alike.

Nonlinear Phenomena in Mathematical Sciences

V. Lakshmikantham
Nonlinear Phenomena in Mathematical Sciences Book PDF

Author : V. Lakshmikantham
Publisher : Elsevier
Page : 1062 pages
File Size : 49,6 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483272054

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Nonlinear Phenomena in Mathematical Sciences by V. Lakshmikantham Pdf

Nonlinear Phenomena in Mathematical Sciences contains the proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, held at the University of Texas at Arlington, on June 16-20,1980. The papers explore trends in nonlinear phenomena in mathematical sciences, with emphasis on nonlinear functional analytic methods and their applications; nonlinear wave theory; and applications to medical and life sciences. In the area of nonlinear functional analytic methods and their applications, the following subjects are discussed: optimal control theory; periodic oscillations of nonlinear mechanical systems; Leray-Schauder degree theory; differential inequalities applied to parabolic and elliptic partial differential equations; bifurcation theory, stability theory in analytical mechanics; singular and ordinary boundary value problems, etc. The following topics in nonlinear wave theory are considered: nonlinear wave propagation in a randomly homogeneous media; periodic solutions of a semilinear wave equation; asymptotic behavior of solutions of strongly damped nonlinear wave equations; shock waves and dissipation theoretical methods for a nonlinear Schr?dinger equation; and nonlinear hyperbolic Volterra equations occurring in viscoelasticity. Applications to medical and life sciences include mathematical modeling in physiology, pharmacokinetics, and neuro-mathematics, along with epidemic modeling and parameter estimation techniques. This book will be helpful to students, practitioners, and researchers in the field of mathematics.

A Course on Nonlinear Waves

S.S. Shen
A Course on Nonlinear Waves Book PDF

Author : S.S. Shen
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401121026

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A Course on Nonlinear Waves by S.S. Shen Pdf

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.