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Solitary Waves in Fluid Media by Atta-ur-Rahman,Iqbal Choudhary Pdf
"Since the first description by John Scott Russel in 1834, the solitary wave phenomenon has attracted considerable interests from scientists. The most interesting discovery since then has been the ability to integrate most of the nonlinear wave equations w"
Solitary Waves in Fluid Media by Claire David,Zhaosheng Feng Pdf
Since the first description by John Scott Russel in 1834, the solitary wave phenomenon has attracted considerable interests from scientists. The most interesting discovery since then has been the ability to integrate most of the nonlinear wave equations which govern solitary waves, from the Korteweg-de Vries equation to the nonlinear Schrodinger equation, in the 1960's. From that moment, a huge amount of theoretical works can be found on solitary waves. Due to the fact that many physical phenomena can be described by a soliton model, applications have followed each other, in telecommunications
Analytical and Numerical Methods for Wave Propagation in Fluid Media by K Murawski Pdf
This book surveys analytical and numerical techniques appropriate to the description of fluid motion with an emphasis on the most widely used techniques exhibiting the best performance. Analytical and numerical solutions to hyperbolic systems of wave equations are the primary focus of the book. In addition, many interesting wave phenomena in fluids are considered using examples such as acoustic waves, the emission of air pollutants, magnetohydrodynamic waves in the solar corona, solar wind interaction with the planet venus, and ion-acoustic solitons. Contents:Mathematical Description of FluidsLinear WavesModel Equations for Weakly Nonlinear WavesAnalytical Methods for Solving the Classical Model Wave EquationsNumerical Methods for a Scalar Hyperbolic EquationsReview of Numerical Methods for Model Wave EquationsNumerical Schemes for a System of One-Dimensional Hyperbolic EquationsA Hyperbolic System of Two-Dimensional EquationsNumerical Methods for the MHD EquationsNumerical Experiments Readership: Researchers in applied and pure mathematics as well as computational and mathematical physics. Keywords:Reviews:“This book tries to fill the gap in the literature by considering together analytical and numerical approaches. The main attention is paid to the wave solutions of the quasi-hyperbolic systems appearing in fluids, plasma, and astrophysics, taking into account the nonlinearity, dispersion, dissipation and randomness of media … It can be useful for students studying the modeling of the wave processes in fluids, plasma and astrophysics.”Professor Efim Pelinovsky Russian Academy of Sciences “The book will be of interest to readers intending to enter this field, and it contains an extensive bibliography that will be useful for readers wishing to widen their study of these topics.”Mathematics Abstracts “I found the book to be very thorough in its description of methods, and the difficulties faced in solving hyperbolic problems … overall I was impressed with this book, and I recommend it as an excellent review source.”Mathematical Reviews
Analytical and Numerical Methods for Wave Propagation in Fluid Media by K. Murawski Pdf
This book surveys analytical and numerical techniques appropriate to the description of fluid motion with an emphasis on the most widely used techniques exhibiting the best performance.Analytical and numerical solutions to hyperbolic systems of wave equations are the primary focus of the book. In addition, many interesting wave phenomena in fluids are considered using examples such as acoustic waves, the emission of air pollutants, magnetohydrodynamic waves in the solar corona, solar wind interaction with the planet venus, and ion-acoustic solitons.
Solitary Waves in Compressible Media by M. C. Shen Pdf
Solitary waves in compressible media of finite depth and infinite depth are studied. The critical speeds are first obtained from the linearized equations and then confirmed by the results of the nonlinear theory. Explicit expressions for the solitary waves are established by a perturbation scheme applied to the nonlinear equations. The case of a polytropic compressible medium of finite depth at rest in the state of equilibrium is studied. Solitary waves in compressible medium of infinite depth are investigated. The former concerns two isothermal layers at rest in the state of equilibrium separated by a contact surface; the latter, an isothermal layer with non-uniform velocity distribution at equilibrium. It is found that solitary waves vanish at certain values of characteristic parameters introduced in each case, and especially no solitary wave solution exists for an isothermal layer of infinite depth. (Author).
Solitary Waves in Dispersive Complex Media by Vasily Y. Belashov,Sergey V. Vladimirov Pdf
Deals with the theoretical, analytical and advanced numerical study of the structure and dynamics of one-dimensional as well as two- and three-dimensional solitons and nonlinear waves described by Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP), nonlinear Schrodinger (NLS) and derivative NLS (DNLS) classes of equations.
Environmental Stratified Flows by Roger Grimshaw Pdf
The dynamics of flows in density-stratified fluids has been and remains now an important topic for scientific enquiry. Such flows arise in many contexts, ranging from industrial settings to the oceanic and atmospheric environments. It is the latter topic which is the focus of this book. Both the ocean and atmosphere are characterised by the basic vertical density stratification, and this feature can affect the dynamics on all scales ranging from the micro-scale to the planetary scale. The aim of this book is to provide a “state-of-the-art” account of stratified flows as they are relevant to the ocean and atmosphere with a primary focus on meso-scale phenomena; that is, on phenomena whose time and space scales are such that the density stratification is a dominant effect, so that frictional and diffusive effects on the one hand and the effects of the earth’s rotation on the other hand can be regarded as of less importance. This in turn leads to an emphasis on internal waves.
Treatise on Geophysics: Mantle Dynamics, Volume 7 aims to provide both a classical and state-of-the-art introduction to the methods and science of mantle dynamics, as well as survey leading order problems (both solved and unsolved) and current understanding of how the mantle works. It is organized around two themes: (1) how is mantle convection studied; and (2) what do we understand about mantle dynamics to date. The first four chapters are thus concerned with pedagogical reviews of the physics of mantle convection; laboratory studies of the fluid dynamics of convection relevant to the mantle; theoretical analysis of mantle dynamics; and numerical analysis and methods of mantle convection. The subsequent chapters concentrate on leading issues of mantle convection itself, which include the energy budget of the mantle; the upper mantle and lithosphere in and near the spreading center (mid-ocean ridge) environment; the dynamics of subducting slabs; hot spots, melting anomalies, and mantle plumes; and finally, geochemical mantle dynamics and mixing. Self-contained volume starts with an overview of the subject then explores each topic in detail Extensive reference lists and cross references with other volumes to facilitate further research Full-color figures and tables support the text and aid in understanding Content suited for both the expert and non-expert
Fluctuation Phenomena: Disorder And Nonlinearity - Proceedings Of The International Workshop by Luis Vazquez,A R Bishop,S Jimenez Pdf
This book addresses the issues of nonlinearity and disorder. It covers mathematical and numerical techniques as well as applications of nonlinearity and disorder. The analysis of continuous and discrete systems is also shown.
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.
The Physics of Composite and Porous Media by T. J. T. (Tim) Spanos,Norman Udey Pdf
Building on the success of T.J.T. Spanos's previous book The Thermophysics of Porous Media, The Physics of Composite and Porous Media explains non-linear field theory that describes how physical processes occur in the earth. It describes physical processes associated with the interaction of the various phases at the macroscale (the scale at which continuum equations are established) and how these interactions give rise to additional physical processes at the megascale (the scale orders of magnitude larger at which a continuum description may once again be established). Details are also given on how experimental, numerical and theoretical work on this subject fits together. This book will be of interest to graduate students and academic researchers working on understanding the physical process in the earth, in addition to those working in the oil and hydrogeology industries.
Waves in Continuous Media by S. L. Gavrilyuk,N.I. Makarenko,S.V. Sukhinin Pdf
Starting with the basic notions and facts of the mathematical theory of waves illustrated by numerous examples, exercises, and methods of solving typical problems Chapters 1 & 2 show e.g. how to recognize the hyperbolicity property, find characteristics, Riemann invariants and conservation laws for quasilinear systems of equations, construct and analyze solutions with weak or strong discontinuities, and how to investigate equations with dispersion and to construct travelling wave solutions for models reducible to nonlinear evolution equations. Chapter 3 deals with surface and internal waves in an incompressible fluid. The efficiency of mathematical methods is demonstrated on a hierarchy of approximate submodels generated from the Euler equations of homogeneous and non-homogeneous fluids. The self-contained presentations of the material is complemented by 200+ problems of different level of difficulty, numerous illustrations, and bibliographical recommendations.
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.
