Nonlinear Waves In Fluids Recent Advances And Modern Applications
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Nonlinear Waves In Fluids Recent Advances And Modern Applications
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Author : Roger Grimshaw
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-23
Nonlinear Waves In Fluids Recent Advances And Modern Applications written by Roger Grimshaw and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-23 with Technology & Engineering categories.
Although nonlinear waves occur in nearly all branches of physics and engi neering, there is an amazing degree of agreement about the fundamental con cepts and the basic paradigms. The underlying unity of the theory for linearized waves is already well-established, with the importance of such universal concepts as group velocity and wave superposition. For nonlinear waves the last few decades have seen the emergence of analogous unifying comcepts. The pervasiveness of the soliton concept is amply demonstrated by the ubiquity of such models as the Korteweg-de Vries equation and the nonlinear Schrodinger equation. Similarly, there is a universality in the study of wave-wave interactions, whether determin istic or statistical, and in the recent developments in the theory of wave-mean flow interactions. The aim of this text is to present the basic paradigms of weakly nonlinear waves in fluids. This book is the outcome of a CISM Summer School held at Udine from September 20-24, 2004. . Like the lectures given there the text covers asymptotic methods for the derivation of canonical evolution equations, such as the Kortew- de Vries and nonlinear Schrodinger equations, descriptions of the basic solution sets of these evolution equations, and the most relevant and compelling applica tions. These themes are interlocked, and this will be demonstrated throughout the text . The topics address any fluid flow application, but there is a bias towards geophysical fluid dynamics, reflecting for the most part the areas where many applications have been found.
Solitary Waves In Fluids
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Author : R. Grimshaw
language : en
Publisher: WIT Press
Release Date : 2007
Solitary Waves In Fluids written by R. Grimshaw and has been published by WIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.
Edited by R.H.J. Grimshaw, this book covers the topic of solitary waves in fluids.
Iutam Symposium On Turbulence In The Atmosphere And Oceans
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Author : David Dritschel
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-09
Iutam Symposium On Turbulence In The Atmosphere And Oceans written by David Dritschel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-09 with Science categories.
The text of the Persian poet Rum ̄ ̄ ?, written some eight centuries ago, and reproduced at the beginning of this book is still relevant to many of our pursuits of knowledge, not least of turbulence. The text illustrates the inability people have in seeing the whole thing, the ‘big picture’. Everybody looks into the problem from his/her vi- point, and that leads to disagreement and controversy. If we could see the whole thing, our understanding would become complete and there would be no cont- versy. The turbulent motion of the atmosphere and oceans, at the heart of the observed general circulation, is undoubtedly very complex and dif?cult to understand in its entirety. Even ‘bare’ turbulence, without rotation and strati?cation whose effects are paramount in the atmosphere and oceans, still poses great fundamental ch- lenges for understanding after a century of research. Rotating strati?ed turbulence is a relatively new research topic. It is also far richer, exhibiting a host of distinct wave types interacting in a complicated and often subtle way with long-lived - herent structures such as jets or currents and vortices. All of this is tied together by basic ?uid-dynamical nonlinearity, and this gives rise to a multitude of phen- ena: spontaneous wave emission, wave-induced transport, both direct and inverse energy scale cascades, lateral and vertical anisotropy, fronts and transport barriers, anomalous transport in coherent vortices, and a very wide range of dynamical and thermodynamical instabilities.
Without Bounds A Scientific Canvas Of Nonlinearity And Complex Dynamics
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Author : Ramon G. Rubio
language : en
Publisher: Springer
Release Date : 2013-05-30
Without Bounds A Scientific Canvas Of Nonlinearity And Complex Dynamics written by Ramon G. Rubio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-30 with Science categories.
Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the research areas covered by the famous Instituto Pluridisciplinar at the Universidad Complutense of Madrid, which he co-founded over two decades ago, and include: fluid physics and related nonlinear phenomena at interfaces and in other geometries, wetting and spreading dynamics, geophysical and astrophysical flows, and novel aspects of electronic transport in anharmonic lattices, as well as topics in neurodynamics and robotics.
Nonlinear Ocean Waves And The Inverse Scattering Transform
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Author : Alfred Osborne
language : en
Publisher: Academic Press
Release Date : 2010-04-07
Nonlinear Ocean Waves And The Inverse Scattering Transform written by Alfred Osborne and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-07 with Science categories.
For more than 200 years, the Fourier Transform has been one of the most important mathematical tools for understanding the dynamics of linear wave trains. Nonlinear Ocean Waves and the Inverse Scattering Transform presents the development of the nonlinear Fourier analysis of measured space and time series, which can be found in a wide variety of physical settings including surface water waves, internal waves, and equatorial Rossby waves. This revolutionary development will allow hyperfast numerical modelling of nonlinear waves, greatly advancing our understanding of oceanic surface and internal waves. Nonlinear Fourier analysis is based upon a generalization of linear Fourier analysis referred to as the inverse scattering transform, the fundamental building block of which is a generalized Fourier series called the Riemann theta function. Elucidating the art and science of implementing these functions in the context of physical and time series analysis is the goal of this book. - Presents techniques and methods of the inverse scattering transform for data analysis - Geared toward both the introductory and advanced reader venturing further into mathematical and numerical analysis - Suitable for classroom teaching as well as research
New Nonlinear Phenomena Research
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Author : Tomas B. Perlidze
language : en
Publisher: Nova Science Publishers
Release Date : 2008
New Nonlinear Phenomena Research written by Tomas B. Perlidze and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This new book focuses on recent and significant research on non-linear, or chaotic behaviour which in real world systems has been reported in electronic circuits and communications systems, chemical reactions, biological behaviour. The applications include solitons, integrable systems, cellular automata, pattern formation, qualitative structure and bifurcation theory, onset of chaos and turbulence, analytic dynamics, and transport phenomena.
Symmetry Phase Modulation And Nonlinear Waves
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Author : Thomas J. Bridges
language : en
Publisher: Cambridge University Press
Release Date : 2017-07-03
Symmetry Phase Modulation And Nonlinear Waves written by Thomas J. Bridges and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-03 with Mathematics categories.
Bridges studies the origin of Korteweg-de Vries equation using phase modulation and its implications in dynamical systems and nonlinear waves.
Analytical Properties Of Nonlinear Partial Differential Equations
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Author : Alexei Cheviakov
language : en
Publisher: Springer Nature
Release Date : 2024-03-22
Analytical Properties Of Nonlinear Partial Differential Equations written by Alexei Cheviakov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-22 with Mathematics categories.
Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will beof interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.
Solitons
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Author : Mohamed Atef Helal
language : en
Publisher: Springer Nature
Release Date : 2022-11-12
Solitons written by Mohamed Atef Helal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-12 with Science categories.
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.
Nonlinear Partial Differential Equations For Scientists And Engineers
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Author : Lokenath Debnath
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-06
Nonlinear Partial Differential Equations For Scientists And Engineers written by Lokenath Debnath and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-06 with Mathematics categories.
The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition, improves on an already highly complete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide.