Solitons in Field Theory and Nonlinear Analysis
Solitons in Field Theory and Nonlinear Analysis

Author: Yisong Yang

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 571

ISBN-13: 1475765487

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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.

Soliton Theory and Its Applications
Soliton Theory and Its Applications

Author: Chaohao Gu

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 414

ISBN-13: 3662031027

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Soliton theory is an important branch of applied mathematics and mathematical physics. An active and productive field of research, it has important applications in fluid mechanics, nonlinear optics, classical and quantum fields theories etc. This book presents a broad view of soliton theory. It gives an expository survey of the most basic ideas and methods, such as physical background, inverse scattering, Backlünd transformations, finite-dimensional completely integrable systems, symmetry, Kac-moody algebra, solitons and differential geometry, numerical analysis for nonlinear waves, and gravitational solitons. Besides the essential points of the theory, several applications are sketched and some recent developments, partly by the authors and their collaborators, are presented.

Topological Solitons
Topological Solitons

Author: Nicholas Manton

Publisher: Cambridge University Press

Published: 2004-06-10

Total Pages: 507

ISBN-13: 1139454692

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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.

Solitons in Mathematics and Physics
Solitons in Mathematics and Physics

Author: Alan C. Newell

Publisher: SIAM

Published: 1985-06-01

Total Pages: 259

ISBN-13: 0898711967

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A discussion of the soliton, focusing on the properties that make it physically ubiquitous and the soliton equation mathematically miraculous.

Theory of Nonlinear Lattices
Theory of Nonlinear Lattices

Author: Morikazu Toda

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 233

ISBN-13: 3642832199

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Soliton theory, the theory of nonlinear waves in lattices composed of particles interacting by nonlinear forces, is treated rigorously in this book. The presentation is coherent and self-contained, starting with pioneering work and extending to the most recent advances in the field. Special attention is focused on exact methods of solution of nonlinear problems and on the exact mathematical treatment of nonlinear lattice vibrations. This new edition updates the material to take account of important new advances.

Solitons
Solitons

Author: P. G. Drazin

Publisher: Cambridge University Press

Published: 1989-02-09

Total Pages: 244

ISBN-13: 9780521336550

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This textbook is an introduction to the theory of solitons in the physical sciences.

Hamiltonian Methods in the Theory of Solitons
Hamiltonian Methods in the Theory of Solitons

Author: Ludwig Faddeev

Publisher: Springer Science & Business Media

Published: 2007-08-10

Total Pages: 602

ISBN-13: 3540699694

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The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.

Nonlinear Waves
Nonlinear Waves

Author: Lokenath Debnath

Publisher: CUP Archive

Published: 1983-12-30

Total Pages: 376

ISBN-13: 9780521254687

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The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.

Optical Solitons
Optical Solitons

Author: Yuri S. Kivshar

Publisher: Academic Press

Published: 2003-06-12

Total Pages: 557

ISBN-13: 0080538096

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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