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Recent Mathematical Methods In Nonlinear Wave Propagation
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Book Synopsis Recent Mathematical Methods in Nonlinear Wave Propagation by : Guy Boillat
Download or read book Recent Mathematical Methods in Nonlinear Wave Propagation written by Guy Boillat and published by Springer. This book was released on 2006-11-14 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Recent Mathematical Methods in Nonlinear Wave Propagation by :
Download or read book Recent Mathematical Methods in Nonlinear Wave Propagation written by and published by . This book was released on 1996 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Regional Research Conference on Mathematical Methods in Nonlinear Wave Propagation Publisher :American Mathematical Soc. ISBN 13 :0821833499 Total Pages :226 pages Book Rating :4.8/5 (218 download)
Book Synopsis Mathematical Studies in Nonlinear Wave Propagation by : Regional Research Conference on Mathematical Methods in Nonlinear Wave Propagation
Download or read book Mathematical Studies in Nonlinear Wave Propagation written by Regional Research Conference on Mathematical Methods in Nonlinear Wave Propagation and published by American Mathematical Soc.. This book was released on 2005 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Non-Linear Wave Propagation With Applications to Physics and Magnetohydrodynamics by A Jeffrey and T Taniuti by :
Download or read book Non-Linear Wave Propagation With Applications to Physics and Magnetohydrodynamics by A Jeffrey and T Taniuti written by and published by Elsevier. This book was released on 2000-04-01 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Ray Methods for Nonlinear Waves in Fluids and Plasmas by : Marcelo Anile
Download or read book Ray Methods for Nonlinear Waves in Fluids and Plasmas written by Marcelo Anile and published by John Wiley & Sons. This book was released on 1993-05-04 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.
Book Synopsis Nonlinear Wave Equations by : Satyanad Kichenassamy
Download or read book Nonlinear Wave Equations written by Satyanad Kichenassamy and published by CRC Press. This book was released on 2021-05-30 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Selected Topics in Nonlinear Wave Mechanics by : C.I. Christov
Download or read book Selected Topics in Nonlinear Wave Mechanics written by C.I. Christov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematics of Wave Propagation by : Julian L. Davis
Download or read book Mathematics of Wave Propagation written by Julian L. Davis and published by Princeton University Press. This book was released on 2021-01-12 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applied Wave Mathematics II by : Arkadi Berezovski
Download or read book Applied Wave Mathematics II written by Arkadi Berezovski and published by Springer Nature. This book was released on 2019-11-16 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical methods for wave propagation in science and engineering by : Mario Durán
Download or read book Mathematical methods for wave propagation in science and engineering written by Mario Durán and published by Ediciones UC. This book was released on 2017 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series of books deals with the mathematical modeling and computational simulation of complex wave propagation phenomena in science and engineering. This first volume of the series introduces the basic mathematical and physical fundamentals, and it is mainly intended as a reference guide and a general survey for scientists and engineers. It presents a broad and practical overview of the involved foundations, being useful as much in industrial research, development, and innovation activities, as in academic labors.
Book Synopsis Asymptotic Methods in Nonlinear Wave Phenomena by : Tommaso Ruggeri
Download or read book Asymptotic Methods in Nonlinear Wave Phenomena written by Tommaso Ruggeri and published by World Scientific. This book was released on 2007 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together several contributions from leading experts in the field of nonlinear wave propagation. This field, which during the last three decades has seen important breakthroughs from the theoretical point of view, has recently acquired increased relevance due to advances in the technology of fluids e.g. at microscale or nanoscale and the recognition of crucial applications to the understanding of biological phenomena.Nonlinear wave theory requires the use of disparate approaches, including formal and rigorous asymptotic methods, Lie group theory, energy methods, numerical analysis, and bifurcation theory. This book presents a unique blend in which different aspects of the theory are enlightened and several real-life applications are investigated. The book will be a valuable resource for applied scientists interested in some of the most recent advances in the theory and in the applications of wave propagation, shock formation, nonequilibrium thermodynamics and energy methods.
Book Synopsis Nonlinear Periodic Waves and Their Modulations by : Anatoli? Mikha?lovich Kamchatnov
Download or read book Nonlinear Periodic Waves and Their Modulations written by Anatoli? Mikha?lovich Kamchatnov and published by World Scientific. This book was released on 2000 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis New Approaches to Nonlinear Waves by : Elena Tobisch
Download or read book New Approaches to Nonlinear Waves written by Elena Tobisch and published by Springer. This book was released on 2015-08-19 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the applicability of these novel methods and approaches to a wide class of evolutionary dispersive PDEs, e.g. equations from Benjamin-Oro, Boussinesq, Hasegawa-Mima, KdV-type, Klein-Gordon, NLS-type, Serre, Shamel , Whitham and Zakharov. This makes the book interesting for professionals in the fields of nonlinear physics, applied mathematics and fluid mechanics as well as students who are studying these subjects. The book can also be used as a basis for a one-semester lecture course in applied mathematics or mathematical physics.
Book Synopsis Asymptotic Methods in Nonlinear Wave Theory by : Alan Jeffrey
Download or read book Asymptotic Methods in Nonlinear Wave Theory written by Alan Jeffrey and published by Pitman Advanced Publishing Program. This book was released on 1982 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Waves by : Lokenath Debnath
Download or read book Nonlinear Waves written by Lokenath Debnath and published by Cambridge University Press. This book was released on 2009-01-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Linear And Nonlinear Wave Propagation by : Spencer P Kuo
Download or read book Linear And Nonlinear Wave Propagation written by Spencer P Kuo and published by World Scientific. This book was released on 2021-04-16 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Waves: A Geometrical Approach by : Angela Slavova
Download or read book Nonlinear Waves: A Geometrical Approach written by Angela Slavova and published by World Scientific Publishing. This book was released on 2018-11-16 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.
