Nonlinear Periodic Waves And Their Modulations An Introductory Course
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Nonlinear Periodic Waves And Their Modulations An Introductory Course
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Author : Anatoly M Kamchatnov
language : en
Publisher: World Scientific
Release Date : 2000-09-05
Nonlinear Periodic Waves And Their Modulations An Introductory Course written by Anatoly M Kamchatnov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-05 with Science categories.
Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions.
Nonlinear Waves
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Author : Peter R. Popivanov
language : en
Publisher: World Scientific
Release Date : 2011
Nonlinear Waves written by Peter R. Popivanov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Big Nate is the star goalie of his school's soccer team, and he is tasked with defending his goal and saving the day against Jefferson Middle School, their archrival.
New Approaches To Nonlinear Waves
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Author : Elena Tobisch
language : en
Publisher: Springer
Release Date : 2015-08-19
New Approaches To Nonlinear Waves written by Elena Tobisch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with Science categories.
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.
Schr Dinger Equations In Nonlinear Systems
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Author : Wu-Ming Liu
language : en
Publisher: Springer
Release Date : 2019-03-20
Schr Dinger Equations In Nonlinear Systems written by Wu-Ming Liu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Science categories.
This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schrödinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose–Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.
Tsunami And Nonlinear Waves
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Author : Anjan Kundu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-19
Tsunami And Nonlinear Waves written by Anjan Kundu 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 2007-06-19 with Science categories.
The need for tsunami research and analysis has grown dramatically following the devastating tsunami of December 2004, which affected Southern Asia. This book pursues a detailed theoretical and mathematical analysis of the fundamentals of tsunamis, especially the evolution and dynamics of tsunamis and other great waves. Of course, it includes specific measurement results from the 2004 tsunami, but the emphasis is on the nature of the waves themselves and their links to nonlinear phenomena.
The Ocean In Motion
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Author : Manuel G. Velarde
language : en
Publisher: Springer
Release Date : 2018-03-28
The Ocean In Motion written by Manuel G. Velarde and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-28 with Science categories.
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.
Rogue And Shock Waves In Nonlinear Dispersive Media
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Author : Miguel Onorato
language : en
Publisher: Springer
Release Date : 2016-09-19
Rogue And Shock Waves In Nonlinear Dispersive Media written by Miguel Onorato and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-19 with Science categories.
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.
Shaping Light In Nonlinear Optical Fibers
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Author : Sonia Boscolo
language : en
Publisher: John Wiley & Sons
Release Date : 2017-05-30
Shaping Light In Nonlinear Optical Fibers written by Sonia Boscolo and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-30 with Technology & Engineering categories.
This book is a contemporary overview of selected topics in fiber optics. It focuses on the latest research results on light wave manipulation using nonlinear optical fibers, with the aim of capturing some of the most innovative developments on this topic. The book’s scope covers both fundamentals and applications from both theoretical and experimental perspectives, with topics including linear and nonlinear effects, pulse propagation phenomena and pulse shaping, solitons and rogue waves, novel optical fibers, supercontinuum generation, polarization management, optical signal processing, fiber lasers, optical wave turbulence, light propagation in disordered fiber media, and slow and fast light. With contributions from leading-edge scientists in the field of nonlinear photonics and fiber optics, they offer an overview of the latest advances in their own research area. The listing of recent research papers at the end of each chapter is useful for researchers using the book as a reference. As the book addresses fundamental and practical photonics problems, it will also be of interest to, and benefit, broader academic communities, including areas such as nonlinear science, applied mathematics and physics, and optical engineering. It offers the reader a wide and critical overview of the state-of-the-art within this practical – as well as fundamentally important and interesting – area of modern science, providing a useful reference which will encourage further research and advances in the field.
Integrable Hamiltonian Hierarchies
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Author : Vladimir Gerdjikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-02
Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov 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 2008-06-02 with Science categories.
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.
A Course On Nonlinear Waves
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Author : S.S. Shen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Course On Nonlinear Waves written by S.S. Shen 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 2012-12-06 with Mathematics categories.
The aim of this book is to give a self-contained introduction to the mathe matical analysis and physical explanations of some basic nonlinear wave phe nomena. This volume grew out of lecture notes for graduate courf;!es which I gave at the University of Alberta, the University of Saskatchewan, ·and Texas A&M University. As an introduction it is not intended to be exhaustive iQ its choice of material, but rather to convey to interested readers a basic; yet practical, methodology as well as some of the more important results obtained since the 1950's. Although the primary purpose of this volume is to serve as a textbook, it should be useful to anyone who wishes to understand or conduct research into nonlinear waves. Here, for the first time, materials on X-ray crystallography and the forced Korteweg-de Vries equation are incorporated naturally into a textbook on non linear waves. Another characteristic feature of the book is the inclusion of four symbolic calculation programs written in MATHEMATICA. They emphasize outcomes rather than numerical methods and provide certain symbolic and nu merical results related to solitons. Requiring only one or two commands to run, these programs have user-friendly interfaces. For example, to get the explicit expression of the 2-soliton of the Korteweg-de Vries equation, one only needs to type in soliton[2] when using the program solipac.m.