Nonlinear Periodic Waves And Their Modulations
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Author | : Anatoly M Kamchatnov |
Publisher | : World Scientific |
Total Pages | : 399 |
Release | : 2000-09-05 |
Genre | : Science |
ISBN | : 9814492434 |
Download Nonlinear Periodic Waves And Their Modulations: An Introductory Course Book in PDF, Epub and Kindle
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 | : Anatoli? Mikha?lovich Kamchatnov |
Publisher | : World Scientific |
Total Pages | : 399 |
Release | : 2000 |
Genre | : Science |
ISBN | : 981024407X |
Download Nonlinear Periodic Waves and Their Modulations Book in PDF, Epub and Kindle
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 | : Francesco Romeo |
Publisher | : Springer Science & Business Media |
Total Pages | : 332 |
Release | : 2013-07-30 |
Genre | : Technology & Engineering |
ISBN | : 3709113091 |
Download Wave Propagation in Linear and Nonlinear Periodic Media Book in PDF, Epub and Kindle
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 | : Thomas J. Bridges |
Publisher | : Cambridge University Press |
Total Pages | : 239 |
Release | : 2017-07-03 |
Genre | : Mathematics |
ISBN | : 1107188849 |
Download Symmetry, Phase Modulation and Nonlinear Waves Book in PDF, Epub and Kindle
Bridges studies the origin of Korteweg-de Vries equation using phase modulation and its implications in dynamical systems and nonlinear waves.
Author | : Peter R. Popivanov |
Publisher | : World Scientific |
Total Pages | : 179 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 9814322121 |
Download Nonlinear Waves Book in PDF, Epub and Kindle
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.
Author | : K Kirchgassner |
Publisher | : World Scientific |
Total Pages | : 430 |
Release | : 1995-08-31 |
Genre | : |
ISBN | : 9814549770 |
Download Structure And Dynamics Of Nonlinear Waves In Fluids: Proceedings Of The Iutam/isimm Symposium Book in PDF, Epub and Kindle
This symposium brought together mechanicians, physicists and applied mathematicians to discuss the interdisciplinary topic of nonlinear wave motion, which displays effects that give rise to a multitude of unanswered questions. Nonlinear waves in fluids in particular display all the prominent nonlinear phenomena such as chaos, turbulence and pattern formation. Amongst the topics emphasized in these proceedings are: travelling fronts, solitary waves and periodic waves (dissipative and conservative); temporal and spatial asymptotics of perturbations of waves; bifurcations, stability and local dynamics of waves; interaction between different waves, and between waves and the mean flow; wave breaking, nonlinear effects on focussing and diffraction; modulation and envelope equations (their derivation and validity); and numerical and experimental results.
Author | : Lokenath Debnath |
Publisher | : World Scientific |
Total Pages | : 683 |
Release | : 1992-09-09 |
Genre | : |
ISBN | : 9814554960 |
Download Nonlinear Dispersive Wave Systems Book in PDF, Epub and Kindle
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 | : Wu-Ming Liu |
Publisher | : Springer |
Total Pages | : 569 |
Release | : 2019-03-20 |
Genre | : Science |
ISBN | : 9811365814 |
Download Schrödinger Equations in Nonlinear Systems Book in PDF, Epub and Kindle
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 | : Michael P. Mortell |
Publisher | : |
Total Pages | : 30 |
Release | : 1970 |
Genre | : |
ISBN | : |
Download Nonlinear Periodic Waves in a Bounded Medium: A Regular Perturbation Approach Book in PDF, Epub and Kindle
A regular perturbation scheme is given for calculating small amplitude nonlinear periodic waves in a medium of finite extent. The first term in the asymptotic expansion is an arbitrary linear standing wave. The signal carried by the waves is determined from the nonlinear terms in the governing equations by an application of the Fredholm alternative. This gives a systematic scheme for calculating the corrections to the basic flow. The first problem considered is the resonant forced motion of a polytropic gas contained in a tube with its end closed. The second problem concerns the free vibration of an anharmonic lattice, or a nonlinear dispersive string. (Author).
Author | : Gabriel Oyibo |
Publisher | : Nova Publishers |
Total Pages | : 182 |
Release | : 2003-10-17 |
Genre | : Mathematics |
ISBN | : 9781590335185 |
Download Advances in Mathematics Research Book in PDF, Epub and Kindle
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.