The Mathematical Theory Of Permanent Progressive Water Waves

Author : Hisashi Okamoto,Mayumi Sh?ji
Publisher : World Scientific
Page : 248 pages
File Size : 48,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9810244509

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The Mathematical Theory of Permanent Progressive Water-waves by Hisashi Okamoto,Mayumi Sh?ji Pdf

This book is a self-contained introduction to the theory of periodic, progressive, permanent waves on the surface of incompressible inviscid fluid. The problem of permanent water-waves has attracted a large number of physicists and mathematicians since Stokes' pioneering papers appeared in 1847 and 1880. Among many aspects of the problem, the authors focus on periodic progressive waves, which mean waves traveling at a constant speed with no change of shape. As a consequence, everything about standing waves are excluded and solitary waves are studied only partly. However, even for this restricted problem, quite a number of papers and books, in physics and mathematics, have appeared and more will continue to appear, showing the richness of the subject. In fact, there remain many open questions to be answered.The present book consists of two parts: numerical experiments and normal form analysis of the bifurcation equations. Prerequisite for reading it is an elementary knowledge of the Euler equations for incompressible inviscid fluid and of bifurcation theory. Readers are also expected to know functional analysis at an elementary level. Numerical experiments are reported so that any reader can re-examine the results with minimal labor: the methods used in this book are well-known and are described as clearly as possible. Thus, the reader with an elementary knowledge of numerical computation will have little difficulty in the re-examination.

Author : J. J. Stoker
Publisher : John Wiley & Sons
Page : 614 pages
File Size : 44,7 Mb
Release : 1992-04-16
Category : Mathematics
ISBN : 9780471570349

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Water Waves by J. J. Stoker Pdf

Offers an integrated account of the mathematical hypothesis of wave motion in liquids with a free surface, subjected to gravitational and other forces. Uses both potential and linear wave equation theories, together with applications such as the Laplace and Fourier transform methods, conformal mapping and complex variable techniques in general or integral equations, methods employing a Green's function. Coverage includes fundamental hydrodynamics, waves on sloping beaches, problems involving waves in shallow water, the motion of ships and much more.

Author : J. J. STOKER
Publisher : Unknown
Page : 0 pages
File Size : 54,7 Mb
Release : 2018
Category : Electronic
ISBN : 1033029165

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WATER WAVES by J. J. STOKER Pdf

Author : James J. Stoker
Publisher : Wiley-Interscience
Page : 128 pages
File Size : 43,7 Mb
Release : 1992
Category : Mathematics
ISBN : 0470828633

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Water Waves by James J. Stoker Pdf

Author : James Johnston Stoker
Publisher : John Wiley & Sons
Page : 608 pages
File Size : 40,9 Mb
Release : 1957
Category : Mathematics
ISBN : UCSD:31822012578035

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Water Waves by James Johnston Stoker Pdf

Offers an integrated account of the mathematical hypothesis of wave motion in liquids with a free surface, subjected to gravitational and other forces. Uses both potential and linear wave equation theories, together with applications such as the Laplace and Fourier transform methods, conformal mapping and complex variable techniques in general or integral equations, methods employing a Green's function. Coverage includes fundamental hydrodynamics, waves on sloping beaches, problems involving waves in shallow water, the motion of ships and much more.

Author : R. S. Johnson
Publisher : Cambridge University Press
Page : 464 pages
File Size : 45,9 Mb
Release : 1997-10-28
Category : Science
ISBN : 0521591724

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A Modern Introduction to the Mathematical Theory of Water Waves by R. S. Johnson Pdf

For over a hundred years, the theory of water waves has been a source of intriguing and often difficult mathematical problems. Virtually every classical mathematical technique appears somewhere within its confines. Beginning with the introduction of the appropriate equations of fluid mechanics, the opening chapters of this text consider the classical problems in linear and nonlinear water-wave theory. This sets the stage for a study of more modern aspects, problems that give rise to soliton-type equations. The book closes with an introduction to the effects of viscosity. All the mathematical developments are presented in the most straightforward manner, with worked examples and simple cases carefully explained. Exercises, further reading, and historical notes on some of the important characters in the field round off the book and make this an ideal text for a beginning graduate course on water waves.

Author : Frederic Dias,Jean-Michel Ghidaglia,Jean-Claude Saut
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 41,7 Mb
Release : 1996
Category : Mouvement ondulatoire, Théorie du
ISBN : 9780821805107

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Mathematical Problems in the Theory of Water Waves by Frederic Dias,Jean-Michel Ghidaglia,Jean-Claude Saut Pdf

The proceedings featured in this book grew out of a conference attended by 40 applied mathematicians and physicists which was held at the International Center for Research in Mathematics in Luminy, France, in May 1995. This volume reviews recent developments in the mathematical theory of water waves. The following aspects are considered: modeling of various wave systems, mathematical and numerical analysis of the full water wave problem (the Euler equations with a free surface) and of asymptotic models (Korteweg-de Vries, Boussinesq, Benjamin-Ono, Davey-Stewartson, Kadomtsev-Petviashvili, etc.), and existence and stability of solitary waves.

Author : Adrian Constantin,Joachim Escher,Robin Stanley Johnson,Gabriele Villari
Publisher : Springer
Page : 228 pages
File Size : 43,8 Mb
Release : 2016-06-28
Category : Mathematics
ISBN : 9783319314624

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Nonlinear Water Waves by Adrian Constantin,Joachim Escher,Robin Stanley Johnson,Gabriele Villari Pdf

This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the material can be used by those who are already familiar with one branch of the study of water waves, to learn more about other areas.

Author : Freddy Dumortier,Henk Broer,Jean Mawhin,Andre Vanderbauwhede,Sjoerd Verduyn Lunel
Publisher : World Scientific
Page : 1184 pages
File Size : 53,9 Mb
Release : 2005-02-23
Category : Science
ISBN : 9789814480918

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EQUADIFF 2003 by Freddy Dumortier,Henk Broer,Jean Mawhin,Andre Vanderbauwhede,Sjoerd Verduyn Lunel Pdf

' This comprehensive volume contains the state of the art on ODE's and PDE's of different nature, functional differential equations, delay equations, and others, mostly from the dynamical systems point of view. A broad range of topics are treated through contributions by leading experts of their fields, presenting the most recent developments. A large variety of techniques are being used, stressing geometric, topological, ergodic and numerical aspects. The scope of the book is wide, ranging from pure mathematics to various applied fields. Examples of the latter are provided by subjects from earth and life sciences, classical mechanics and quantum-mechanics, among others. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents: Computational Aspects of Differential Equations and ApplicationsWater WavesTopological and Variational MethodsQualitative Theory of Nonlinear Parabolic and Elliptic EquationsAround Hilbert's 16th ProblemNavier–Stokes Equations and Reaction Diffusion EquationsHyperbolic Dynamics and BeyondSymmetry and MechanicsShock Waves and Conservation LawsNonlinear Elliptic Partial Differential EquationsAlgebraic Aspects and Optimisation in Dynamical SystemsCase Studies in Theoretical Interpretation of Numerical ExperimentsInfinite-Dimensional DynamicsQuasiperiodicityDelay EquationsWave Stability and Pattern FormationNonautonomous DynamicsNormal Forms and Invariant ManifoldsSingular PerturbationsDifferential Geometric Foliations and FlowsHomoclinic and Heteroclinic DynamicsMathematical Aspects of Celestical Mechanics Readership: Graduate students and researchers in mathematics, especially in ODE and PDE areas. Keywords:Differential Equations;Dynamical Systems;ODE;PDE;Delay Equations;Water Waves;Hilbert''s 16th Problem'

Author : David Lannes
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 40,5 Mb
Release : 2013-05-08
Category : Mathematics
ISBN : 9780821894705

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The Water Waves Problem by David Lannes Pdf

This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.

Author : Thomas J. Bridges,Mark D. Groves,David P. Nicholls
Publisher : Cambridge University Press
Page : 299 pages
File Size : 51,6 Mb
Release : 2016-02-04
Category : Mathematics
ISBN : 9781107565562

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Lectures on the Theory of Water Waves by Thomas J. Bridges,Mark D. Groves,David P. Nicholls Pdf

A range of experts contribute introductory-level lectures on active topics in the theory of water waves.

Author : Elena Kartashova
Publisher : Cambridge University Press
Page : 241 pages
File Size : 51,6 Mb
Release : 2010-10-21
Category : Science
ISBN : 9781139493086

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Nonlinear Resonance Analysis by Elena Kartashova Pdf

Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780521763608.

Author : Matiur Rahman
Publisher : Unknown
Page : 368 pages
File Size : 51,5 Mb
Release : 1995-01-19
Category : Mathematics
ISBN : UOM:39015032308077

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Water Waves by Matiur Rahman Pdf

Self-contained and accessible, Water Waves provides an up-to-date introduction to the mathematical and physical aspects of water wave theory. Written particularly for undergraduates engineering, physics, and mathematics students, the book contains a wealth of examples and exercises. It begins with the derivations of the fundamental mathematical equations, outlining differential equations appropriate for the description of physical phenomena. It goes on to detail the development of wave equations (including the essential boundary conditions), and to describe small amplitude wave theory, finite amplitude wave theory, tidal dynamics in shallow water, wave statistics and the wave energy spectrum, and nonlinear long waves in shallow water. The book concludes with a description of the inverse scattering technique used to solve solitary wave problems. Rigorous and coherent, Water Waves is ideal for students and professionals approaching the subject for the first time.

Author : B. N. Mandal
Publisher : WIT Press (UK)
Page : 376 pages
File Size : 51,8 Mb
Release : 1997
Category : Fluid mechanics
ISBN : UCSD:31822026145698

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Mathematical Techniques for Water Waves by B. N. Mandal Pdf

The mathematical techniques used to handle various water wave problems are varied and fascinating. This book highlights a number of these techniques in connection with investigations of some classes of water wave problems by leading researchers in this field. The first eight chapters discuss linearised theory while the last two cover nonlinear analysis. This book will be an invaluable source of reference for advanced mathematical work in water wave theory.

Author : Anonim
Publisher : World Scientific
Page : 444 pages
File Size : 45,8 Mb
Release : 2009
Category : Fluid dynamics
ISBN : 9789814282253

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Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) by Anonim Pdf

"This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems. In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics."-