Nonlinear Periodic Waves And Their Modulations

Author : A M Kamchatnov
Publisher : World Scientific
Page : 396 pages
File Size : 43,9 Mb
Release : 2000-09-05
Category : Science
ISBN : 9789814492430

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Nonlinear Periodic Waves and Their Modulations by A M Kamchatnov Pdf

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. Contents:Introduction and Basic ConceptsNonlinear Wave Equations in PhysicsWhitham Theory of ModulationsComplete Integrability of Nonlinear Wave EquationsPeriodic SolutionsDissipationless Shock WaveNonlinear Theory of Modulational InstabilityAppendices:Some Formulas from the Theory of Elliptic FunctionsAlgebraic Resolvents of Fourth Degree PolynomialsSolutions to Exercises Readership: Advanced graduate students and young researchers in nonlinear wave theory. Keywords:Nonlinear Waves;Solitons;Integrable Equations;Inverse Scattering Transform;Periodic Solutions;Whitham Theory;Modulation;Hodograph Transform;Dissipationless Shock Waves;Modulational Instability

Author : Anatoli? Mikha?lovich Kamchatnov
Publisher : World Scientific
Page : 399 pages
File Size : 48,8 Mb
Release : 2000
Category : Science
ISBN : 9789810244071

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Nonlinear Periodic Waves and Their Modulations by Anatoli? Mikha?lovich Kamchatnov Pdf

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.

Author : Thomas J. Bridges
Publisher : Cambridge University Press
Page : 239 pages
File Size : 45,6 Mb
Release : 2017-07-03
Category : Mathematics
ISBN : 9781107188846

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Symmetry, Phase Modulation and Nonlinear Waves by Thomas J. Bridges Pdf

Bridges studies the origin of Korteweg-de Vries equation using phase modulation and its implications in dynamical systems and nonlinear waves.

Author : Wu-Ming Liu,Emmanuel Kengne
Publisher : Springer
Page : 569 pages
File Size : 44,8 Mb
Release : 2019-03-20
Category : Science
ISBN : 9789811365812

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Schrödinger Equations in Nonlinear Systems by Wu-Ming Liu,Emmanuel Kengne Pdf

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.

Author : Francesco Romeo,Massimo Ruzzene
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 47,6 Mb
Release : 2013-07-30
Category : Technology & Engineering
ISBN : 9783709113097

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Wave Propagation in Linear and Nonlinear Periodic Media by Francesco Romeo,Massimo Ruzzene Pdf

Waves and defect modes in structures media.- Piezoelectric superlattices and shunted periodic arrays as tunable periodic structures and metamaterials.- Topology optimization.- Map-based approaches for periodic structures.- Methodologies for nonlinear periodic media.​ The contributions in this volume present both the theoretical background and an overview of the state-of-the art in wave propagation in linear and nonlinear periodic media in a consistent format. They combine the material issued from a variety of engineering applications, spanning a wide range of length scale, characterized by structures and materials, both man-made and naturally occurring, featuring geometry, micro-structural and/or materials properties that vary periodically in space, including periodically stiffened plates, shells and beam-like as well as bladed disc assemblies, phononic metamaterials, photonic crystals and ordered granular media. Along with linear models and applications, analytical methodologies for analyzing and exploiting complex dynamical phenomena arising in nonlinear periodic systems are also presented.​

Author : Miguel Onorato,Stefania Resitori,Fabio Baronio
Publisher : Springer
Page : 370 pages
File Size : 49,9 Mb
Release : 2016-09-19
Category : Science
ISBN : 9783319392141

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Rogue and Shock Waves in Nonlinear Dispersive Media by Miguel Onorato,Stefania Resitori,Fabio Baronio Pdf

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.

Author : Manuel G. Velarde,Roman Yu. Tarakanov,Alexey V. Marchenko
Publisher : Springer
Page : 625 pages
File Size : 40,8 Mb
Release : 2018-03-28
Category : Science
ISBN : 9783319719344

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The Ocean in Motion by Manuel G. Velarde,Roman Yu. Tarakanov,Alexey V. Marchenko Pdf

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.

Author : Anjan Kundu
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 42,6 Mb
Release : 2007-06-19
Category : Science
ISBN : 9783540712565

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Tsunami and Nonlinear Waves by Anjan Kundu Pdf

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.

Author : Fatkhulla Abdullaev,Vladimir V. Konotop
Publisher : Springer Science & Business Media
Page : 563 pages
File Size : 41,5 Mb
Release : 2006-03-02
Category : Science
ISBN : 9781402021909

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Nonlinear Waves: Classical and Quantum Aspects by Fatkhulla Abdullaev,Vladimir V. Konotop Pdf

Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices (including quantum and nonlinear lattices), and nonlinear optics and photonics. Classical and quantum aspects of the dynamics of nonlinear waves are considered. The contributions focus on the Gross-Pitaevskii equation and on the quantum nonlinear Schrödinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.

Author : Sonia Boscolo,Christophe Finot
Publisher : John Wiley & Sons
Page : 486 pages
File Size : 41,7 Mb
Release : 2017-05-30
Category : Technology & Engineering
ISBN : 9781119088127

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Shaping Light in Nonlinear Optical Fibers by Sonia Boscolo,Christophe Finot Pdf

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.

Author : Lokenath Debnath
Publisher : World Scientific
Page : 683 pages
File Size : 46,8 Mb
Release : 1992-09-09
Category : Electronic
ISBN : 9789814554961

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Nonlinear Dispersive Wave Systems by Lokenath Debnath Pdf

This book brings together a comprehensive account of major developments in the theory and applications of nonlinear dispersive waves, nonlinear water waves, KdV and nonlinear Schrodinger equations, Davey-Stewartson equation, Benjamin-Ono equation and nonlinear instability phenomena. In order to give the book a wider readership, chapters have been written by internationally known researchers who have made significant contributions to nonlinear waves and nonlinear instability. This volume will be invaluable to applied mathematicians, physicists, geophysicists, oceanographers, engineering scientists, and to anyone interested in nonlinear dynamics.

Author : Seymour Brian R,Mortell Michael P
Publisher : World Scientific
Page : 420 pages
File Size : 50,9 Mb
Release : 2017-01-18
Category : Technology & Engineering
ISBN : 9789813100350

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Nonlinear Waves In Bounded Media: The Mathematics Of Resonance by Seymour Brian R,Mortell Michael P Pdf

This unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent. It involves both standing (unforced) waves and resonant oscillations due to external periodic forcing. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media. The examples used come mainly from gas dynamics, water waves and viscoelastic waves.

Author : Vladimir Gerdjikov,Gaetano Vilasi,Alexandar Borisov Yanovski
Publisher : Springer Science & Business Media
Page : 645 pages
File Size : 51,6 Mb
Release : 2008-06-02
Category : Science
ISBN : 9783540770534

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Integrable Hamiltonian Hierarchies by Vladimir Gerdjikov,Gaetano Vilasi,Alexandar Borisov Yanovski Pdf

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.

Author : Gabriel Oyibo
Publisher : Nova Publishers
Page : 182 pages
File Size : 45,6 Mb
Release : 2003-10-17
Category : Mathematics
ISBN : 159033518X

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Advances in Mathematics Research by Gabriel Oyibo Pdf

Mathematics has been behind many of humanity's most significant advances in fields as varied as genome sequencing, medical science, space exploration, and computer technology. But those breakthroughs were yesterday. Where will mathematicians lead us tomorrow and can we help shape that destiny? This book assembles carefully selected articles highlighting and explaining cutting-edge research and scholarship in mathematics. Contents: Preface; Solvability of Quasilinear Elliptic Second Order Differential Equations in Rn without Condition at Infinity; Recent Topics on a Class of Nonlinear Integrodifferential Equations of Physical Significance'; Nonparametric Estimation with Censored Observations; Normalisers of Groups Commensurable with PSL2(Z); Spectral Analysis of a Class of Multigroup Neutron Transport Operators in Slab Geometry; Extremum of a Nonlocal Functional Depending on Higher Order Derivatives of the Unknown Function; On Quantum Conditional Probability Spaces; Index.

Author : Petar Radoev Popivanov
Publisher : Unknown
Page : 179 pages
File Size : 47,7 Mb
Release : 2010
Category : Electronic
ISBN : 9814340529

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Nonlinear Waves by Petar Radoev Popivanov Pdf