Download or read book Solitary Waves in Fluid Media written by Atta-ur-Rahman and published by . This book was released on 2010-09-10 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"
Download or read book Solitary Waves in Fluid Media written by Claire David and published by Bentham Science Publishers. This book was released on 2010 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Solitary Waves in Fluids written by R. Grimshaw and published by WIT Press. This book was released on 2007 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited by R.H.J. Grimshaw, this book covers the topic of solitary waves in fluids.
Download or read book Environmental Stratified Flows written by Roger Grimshaw and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analytical and Numerical Methods for Wave Propagation in Fluid Media written by K. Murawski and published by World Scientific. This book was released on 2002 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analytical And Numerical Methods For Wave Propagation In Fluid Media written by Krzysztof Murawski and published by World Scientific. This book was released on 2002-11-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Download or read book Weakly Nonlocal Solitary Waves and Beyond All Orders Asymptotics written by John P. Boyd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.
Download or read book Solitary Waves in Compressible Media written by M. C. Shen and published by . This book was released on 1964 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
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.
Download or read book Internal Gravity Waves written by Bruce R. Sutherland and published by Cambridge University Press. This book was released on 2010-09-02 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of internal gravity waves provides many challenges: they move along interfaces as well as in fully three-dimensional space, at relatively fast temporal and small spatial scales, making them difficult to observe and resolve in weather and climate models. Solving the equations describing their evolution poses various mathematical challenges associated with singular boundary value problems and large amplitude dynamics. This book provides the first comprehensive treatment of the theory for small and large amplitude internal gravity waves. Over 120 schematics, numerical simulations and laboratory images illustrate the theory and mathematical techniques, and 130 exercises enable the reader to apply their understanding of the theory. This is an invaluable single resource for academic researchers and graduate students studying the motion of waves within the atmosphere and ocean, and also mathematicians, physicists and engineers interested in the properties of propagating, growing and breaking waves.
Download or read book Solitary Waves in Dispersive Complex Media written by Vasily Y. Belashov and published by Springer Science & Business Media. This book was released on 2006-01-20 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Ocean in Motion written by Manuel G. Velarde and published by Springer. This book was released on 2018-03-28 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book commemorates the 70th birthday of Eugene Morozov, the noted Russian observational oceanographer. It contains many contributions reflecting his fields of interest, including but not limited to tidal internal waves, ocean circulation, deep ocean currents, and Arctic oceanography. Special attention is paid to studies on internal waves and especially those on tidal internal waves in the Global Ocean. These papers describe the most important open problems concerning experimental studies of internal waves and their theoretical, numerical, and laboratory modeling. Further contributions investigate the physics of surface waves and their interaction with internal waves. Here, the focus is on describing interaction processes between internal waves and deep currents in the ocean, especially currents of Antarctic Bottom Water in abyssal fractures. They also touch on the problem of oceanic circulation and related processes in fjords, including those occurring under sea ice. Given its breadth of coverage, the book will appeal to anyone interested in a survey of ocean dynamics, ranging from historic perspectives to modern research topics.
Download or read book Waves on Fluid Interfaces written by Richard E. Meyer and published by Academic Press. This book was released on 2014-05-10 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Research Center Symposium: Waves on Fluid Interfaces covers the proceedings of a symposium conducted by the Mathematics Research Center of the University of Wisconsin-Madison on October 18-20, 1982. The book focuses on nonlinear instabilities of classical interfaces, physical structure of real interfaces, and the challenges these reactions pose to the understanding of fluids. The selection first elaborates on finite-amplitude interfacial waves, instability of finite-amplitude interfacial waves, and finite-amplitude water waves with surface tension. Discussions focus on reformulation as an integro-differential equation, perturbation solutions, results for interfacial waves with current jump, wave of zero height, weakly nonlinear waves, and numerical methods. The text then takes a look at generalized vortex methods for free-surface flows; a review of solution methods for viscous flow in the presence of deformable boundaries; and existence criteria for fluid interfaces in the absence of gravity. The book ponders on the endothelial interface between tissue and blood, moving contact line, rupture of thin liquid films, film waves, and interfacial instabilities caused by air flow over a thin liquid layer. Topics include stability analysis of liquid film, interpretation of film instabilities, simple film, linear stability theory, inadequacy of the usual hydrodynamic model, and marcomolecule transport across the artery wall. The selection is a valuable source of data for researchers interested in the reactions of waves on fluid interfaces.
Download or read book Physics of Solitons written by Thierry Dauxois and published by Cambridge University Press. This book was released on 2006-03-09 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook gives an instructive view of solitons and their applications for advanced students of physics.
Download or read book Partial Differential Equations and Solitary Waves Theory written by Abdul-Majid Wazwaz and published by Springer Science & Business Media. This book was released on 2010-05-28 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.
Download or read book Localization And Solitary Waves In Solid Mechanics written by Alan R Champneys and published by World Scientific. This book was released on 1999-11-30 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classical problems such as the buckling of cylindrical shells, twisted rods and pipelines, to the folding of geological strata, the failure of sandwich structures and the propagation of solitary waves in suspended beam systems.
