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Author: P. G. Drazin
Publisher: Cambridge University Press
ISBN: 9780521336550
Category : Mathematics
Languages : en
Pages : 244
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Book Description
This textbook is an introduction to the theory of solitons in the physical sciences.
Author: P. G. Drazin
Publisher: Cambridge University Press
ISBN: 9780521336550
Category : Mathematics
Languages : en
Pages : 244
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Book Description
This textbook is an introduction to the theory of solitons in the physical sciences.
Author: Yuri S. Kivshar
Publisher: Academic Press
ISBN: 0080538096
Category : Technology & Engineering
Languages : en
Pages : 557
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Book Description
The current research into solitons and their use in fiber optic communications is very important to the future of communications. Since the advent of computer networking and high speed data transmission technology people have been striving to develop faster and more reliable communications media. Optical pulses tend to broaden over relatively short distances due to dispersion, but solitons on the other hand are not as susceptible to the effects of dispersion, and although they are subject to losses due to attenuation they can be amplified without being received and re-transmitted.This book is the first to provide a thorough overview of optical solitons. The main purpose of this book is to present the rapidly developing field of Spatial Optical Solitons starting from the basic concepts of light self-focusing and self-trapping. It will introduce the fundamental concepts of the theory of nonlinear waves and solitons in non-integrated but physically realistic models of nonlinear optics including their stability and dynamics. Also, it will summarize a number of important experimental verification of the basic theoretical predictions and concepts covering the observation of self-focusing in the earlier days of nonlinear optics and the most recent experimental results on spatial solitons, vortex solitons, and soliton interaction & spiraling.* Introduces the fundamental concepts of the theory of nonlinear waves and solitons through realistic models * Material is based on authors' years of experience actively working in and researching the field* Summarizes the most important experimental verification of the basic theories, predictions and concepts of this ever evolving field from the earliest studies to the most recent
Author: Michel Remoissenet
Publisher: Springer Science & Business Media
ISBN: 3662030578
Category : Science
Languages : en
Pages : 248
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Book Description
Nonlinearity is a fascinating element of nature whose importance has been appreciated for many years when considering large-amplitude wave motions observed in various fields ranging from fluids and plasmas to solid-state, chemical, biological, and geological systems. Localized large-amplitude waves called solitons, which propagate without spreading and have particle-like properties, represent one of the most striking aspects of nonlinear phenomena. Although a wealth of literature on the subject, including theoretical and numerical studies, is available in good recent books and research journals, very little material has found its way into introductory texbooks and curricula. This is perhaps due to a belief that nonlinear physics is difficult and cannot be taught at an introductory level to undergraduate students and practitioners. Consequently, there is considerable interest in developing practical material suitable for students, at the lowest introductory level. This book is intended to be an elementary introduction to the physics of solitons, for students, physicists, engineers and practitioners. We present the modeling of nonlinear phenomena where soliton-like waves are involved, together with applications to a wide variety of concrete systems and experiments. This book is designed as a book of physical ideas and basic methods and not as an up-to-the minute book concerned with the latest research results. The background in physics and the amount of mathematical knowledge assumed of the reader is within that usually accumulated by junior or senior students in physics.
Author: Nicholas Manton
Publisher: Cambridge University Press
ISBN: 1139454692
Category : Science
Languages : en
Pages : 507
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Book Description
Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several field theories.
Author: Linn F. Mollenauer
Publisher: Elsevier
ISBN: 0080465064
Category : Technology & Engineering
Languages : en
Pages : 297
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Book Description
Solitons are waves that retain their form through obstacle and distance. Solitons can be found in hydrodynamics, nonlinear optics, plasma physics, and biology. Optical solitons are solitary light waves that hold their form over an expansive interval. Conservation of this form creates an effective model for long distance voice and data transmission.The application of this principle is essential to the technology of wired communications. Optical solitons produce crystal clear phone calls cross-country and internationally. It is because of these that someone on the other end of the phone sounds 'in the next room.' It is also pertinent to high-speed network information transmittal.Mollenauer and Gordon have written the only text that an engineer or graduate student will need to understand this foundation subject in optics.*Written by Linn Mollenauer and James Gordon who are celebrated for applying optical solitons to telecommnications*Combines mathematical developments with well-chosen practical examples and design formulas*Extensive material on the basic physics of fiber optic transmission and its practical applications
Author: Thierry Dauxois
Publisher: Cambridge University Press
ISBN: 0521854210
Category : Mathematics
Languages : en
Pages : 435
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Book Description
This textbook gives an instructive view of solitons and their applications for advanced students of physics.
Author: Allan P. Fordy
Publisher: Manchester University Press
ISBN: 9780719014918
Category : Mathematics
Languages : en
Pages : 472
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Book Description
A coherent introduction to the complete range of soliton theory including Hirota's method and Backlund transformations. Details physical applications of soliton theory with chapters on the peculiar wave patterns of the Andaman Sea, atmospheric phenomena, general relativity and Davydov solitons. Contains testing for full integrability, a discussion of the Painlevé technique, symmetries and conservation law.
Author: Yisong Yang
Publisher: Springer Science & Business Media
ISBN: 1475765487
Category : Mathematics
Languages : en
Pages : 571
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Book Description
There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.
Author: Eryk Infeld
Publisher: Cambridge University Press
ISBN: 9780521635578
Category : Mathematics
Languages : en
Pages : 416
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Book Description
The second edition of a highly successful book on nonlinear waves, solitons and chaos.
Author: Mohamed Atef Helal
Publisher: Springer Nature
ISBN: 1071624571
Category : Science
Languages : en
Pages : 483
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Book Description
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.
