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Solitons in Field Theory and Nonlinear Analysis

2013-03-14 Mathematics
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Release : 2013-03-14
Genre : Mathematics
Kind : eBook
Book Rating : 487/5 ( reviews)

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Book Synopsis Solitons in Field Theory and Nonlinear Analysis by : Yisong Yang

Download or read book Solitons in Field Theory and Nonlinear Analysis written by Yisong Yang. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topological and Non-Topological Solitons in Scalar Field Theories

2018-07-26 Science
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Release : 2018-07-26
Genre : Science
Kind : eBook
Book Rating : 154/5 ( reviews)

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Book Synopsis Topological and Non-Topological Solitons in Scalar Field Theories by : Yakov M. Shnir

Download or read book Topological and Non-Topological Solitons in Scalar Field Theories written by Yakov M. Shnir. This book was released on 2018-07-26. Available in PDF, EPUB and Kindle. Book excerpt: Solitons emerge in various non-linear systems as stable localized configurations, behaving in many ways like particles, from non-linear optics and condensed matter to nuclear physics, cosmology and supersymmetric theories. This book provides an introduction to integrable and non-integrable scalar field models with topological and non-topological soliton solutions. Focusing on both topological and non-topological solitons, it brings together debates around solitary waves and construction of soliton solutions in various models and provides a discussion of solitons using simple model examples. These include the Kortenweg-de-Vries system, sine-Gordon model, kinks and oscillons, and skyrmions and hopfions. The classical field theory of scalar field in various spatial dimensions is used throughout the book in presentation of related concepts, both at the technical and conceptual level. Providing a comprehensive introduction to the description and construction of solitons, this book is ideal for researchers and graduate students in mathematics and theoretical physics.

Soliton Theory and Its Applications

2013-03-14 Mathematics
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Release : 2013-03-14
Genre : Mathematics
Kind : eBook
Book Rating : 027/5 ( reviews)

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Book Synopsis Soliton Theory and Its Applications by : Chaohao Gu

Download or read book Soliton Theory and Its Applications written by Chaohao Gu. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: 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

2004-06-10 Science
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Release : 2004-06-10
Genre : Science
Kind : eBook
Book Rating : 692/5 ( reviews)

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Book Synopsis Topological Solitons by : Nicholas Manton

Download or read book Topological Solitons written by Nicholas Manton. This book was released on 2004-06-10. Available in PDF, EPUB and Kindle. Book excerpt: 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, Nonlinear Evolution Equations and Inverse Scattering

1991-12-12 Mathematics
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Release : 1991-12-12
Genre : Mathematics
Kind : eBook
Book Rating : 302/5 ( reviews)

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Book Synopsis Solitons, Nonlinear Evolution Equations and Inverse Scattering by : Mark J. Ablowitz

Download or read book Solitons, Nonlinear Evolution Equations and Inverse Scattering written by Mark J. Ablowitz. This book was released on 1991-12-12. Available in PDF, EPUB and Kindle. Book excerpt: This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

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