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A Modern Introduction To The Mathematical Theory Of Water Waves
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Book Synopsis A Modern Introduction to the Mathematical Theory of Water Waves by : Robin Stanley Johnson
Download or read book A Modern Introduction to the Mathematical Theory of Water Waves written by Robin Stanley Johnson and published by Cambridge University Press. This book was released on 1997-10-28 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text considers classical and modern problems in linear and non-linear water-wave theory.
Book Synopsis Water Waves: The Mathematical Theory with Applications by : James Johnston Stoker
Download or read book Water Waves: The Mathematical Theory with Applications written by James Johnston Stoker and published by Courier Dover Publications. This book was released on 2019-04-17 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1957, this is a classic monograph in the area of applied mathematics. It offers a connected account of the mathematical theory of wave motion in a liquid with a free surface and subjected to gravitational and other forces, together with applications to a wide variety of concrete physical problems. A never-surpassed text, it remains of permanent value to a wide range of scientists and engineers concerned with problems in fluid mechanics. The four-part treatment begins with a presentation of the derivation of the basic hydrodynamic theory for non-viscous incompressible fluids and a description of the two principal approximate theories that form the basis for the rest of the book. The second section centers on the approximate theory that results from small-amplitude wave motions. A consideration of problems involving waves in shallow water follows, and the text concludes with a selection of problems solved in terms of the exact theory. Despite the diversity of its topics, this text offers a unified, readable, and largely self-contained treatment.
Book Synopsis The Mathematical Theory of Permanent Progressive Water-Waves by : Hisashi Okamoto
Download or read book The Mathematical Theory of Permanent Progressive Water-Waves written by Hisashi Okamoto and published by World Scientific Publishing Company. This book was released on 2001-09-28 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Water Waves written by Matiur Rahman and published by . This book was released on 1995-01-19 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Hydrodynamics and Water Waves by : Bernard LeMéhauté
Download or read book An Introduction to Hydrodynamics and Water Waves written by Bernard LeMéhauté and published by . This book was released on 1969 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on the Theory of Water Waves by : Thomas J. Bridges
Download or read book Lectures on the Theory of Water Waves written by Thomas J. Bridges and published by Cambridge University Press. This book was released on 2016-02-04 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A range of experts contribute introductory-level lectures on active topics in the theory of water waves.
Book Synopsis Nonlinear Water Waves by : Adrian Constantin
Download or read book Nonlinear Water Waves written by Adrian Constantin and published by Springer. This book was released on 2016-06-28 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis by : Adrian Constantin
Download or read book Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis written by Adrian Constantin and published by SIAM. This book was released on 2011-01-01 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Water Waves Problem by : David Lannes
Download or read book The Water Waves Problem written by David Lannes and published by American Mathematical Soc.. This book was released on 2013-05-08 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Journal of Nonlinear Mathematical Physics Vol. 14 by :
Download or read book Journal of Nonlinear Mathematical Physics Vol. 14 written by and published by atlantis press. This book was released on with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Journal of Nonlinear Mathematical Physics by :
Download or read book Journal of Nonlinear Mathematical Physics written by and published by atlantis press. This book was released on with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 309 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 Nonlinear Dispersive Waves by : David Henry
Download or read book Nonlinear Dispersive Waves written by David Henry and published by Springer Nature. This book was released on with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic and Parabolic Equations by : Joachim Escher
Download or read book Elliptic and Parabolic Equations written by Joachim Escher and published by Springer. This book was released on 2015-06-04 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The international workshop on which this proceedings volume is based on brought together leading researchers in the field of elliptic and parabolic equations. Particular emphasis was put on the interaction between well-established scientists and emerging young mathematicians, as well as on exploring new connections between pure and applied mathematics. The volume contains material derived after the workshop taking up the impetus to continue collaboration and to incorporate additional new results and insights.
Book Synopsis Extreme Ocean Waves by : Efim Pelinovsky
Download or read book Extreme Ocean Waves written by Efim Pelinovsky and published by Springer. This book was released on 2015-09-02 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and updated second edition details the vast progress that has been achieved in the understanding of the physical mechanisms of rogue wave phenomenon in recent years. The selected articles address such issues as the formation of rogue waves due to modulational instability of nonlinear wave field, physical and statistical properties of extreme ocean wave generation in deep water as well as in shallow water, various models of nonlinear water waves, special analysis of nonlinear resonances between water waves and the relation between in situ observations, experimental data and rogue wave theories. In addition, recent results on tsunami waves due to subaerial landslides are presented. This book is written for specialists in the fields of fluid mechanics, applied mathematics, nonlinear physics, physical oceanography and geophysics, and for students learning these subjects.
Download or read book Solitons written by Mohamed Atef Helal and published by Springer Nature. This book was released on 2022-11-12 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.
Book Synopsis Linear Partial Differential Equations for Scientists and Engineers by : Tyn Myint-U
Download or read book Linear Partial Differential Equations for Scientists and Engineers written by Tyn Myint-U and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry; solutions are provided.
