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Topological Solitons

Author: Nicholas Manton

Publisher: Cambridge University Press

Published: 2004-06-10

Total Pages: 507

ISBN-13: 1139454692

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.

Topological and Non-Topological Solitons in Scalar Field Theories

Author: Yakov M. Shnir

Publisher: Cambridge University Press

Published: 2018-07-26

Total Pages: 281

ISBN-13: 1316997154

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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.

Topological and Non-Topological Solitons in Scalar Field Theories

Author: Yakov M. Shnir

Publisher: Cambridge University Press

Published: 2018-07-26

Total Pages: 281

ISBN-13: 1108429912

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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, this book brings together discussion of solitary waves and construction of soliton solutions and provides a discussion of solitons using simple model examples.

Dynamics of Topological Magnetic Solitons

Author: Victor G. Bar'yakhtar

Publisher: Springer

Published: 2006-04-11

Total Pages: 189

ISBN-13: 3540478256

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Dynamics of Topological Magnetic Solitons gives a theoretical and experimental review of the dynamics of high-speed domain walls and Bloch lines. After the introduction of magnetic solitons, experimental methods for the observation of the dynamics of domain walls are presented. Further chapters discuss main features of the stimulated motion of domain walls, their magnetoelastic interaction, stability and relaxation. Finally, the dynamics of domain walls in weak ferromagnets with more than one dimension is treated. The last chapter presents the dynamics of Bloch lines and their clusters. More than 230 references guide the reader to the literature. Physicists will gain new insights in interesting applications of soliton theory in condensed matter physics. Engineers will find new information on magnetooptical effects for further applications.

Solitons

Author: R. MacKenzie

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 308

ISBN-13: 1461212545

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Solitons were discovered by John Scott Russel in 1834, and have interested scientists and mathematicians ever since. They have been the subject of a large body of research in a wide variety of fields of physics and mathematics, not to mention engineering and other branches of science such as biology. This volume comprises the written versions of the talks presented at a workshop held at Queen's University in 1997, an interdisciplinary meeting wherein top researchers from many fields could meet, interact, and exchange ideas. Topics covered include mathematical and numerical aspects of solitons, as well as applications of solitons to nuclear and particle physics, cosmology, and condensed-matter physics. The book should be of interest to researchers in any field in which solitons are encountered.

Solitons

Author: Boling Guo

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-03-19

Total Pages: 376

ISBN-13: 3110549417

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This book provides an up-to-date overview of mathematical theories and research results on solitons, presenting related mathematical methods and applications as well as numerical experiments. Different types of soliton equations are covered along with their dynamical behaviors and applications from physics, making the book an essential reference for researchers and graduate students in applied mathematics and physics. Contents Introduction Inverse scattering transform Asymptotic behavior to initial value problems for some integrable evolution nonlinear equations Interaction of solitons and its asymptotic properties Hirota method Bäcklund transformations and the infinitely many conservation laws Multi-dimensional solitons and their stability Numerical computation methods for some nonlinear evolution equations The geometric theory of solitons Global existence and blow up for the nonlinear evolution equations The soliton movements of elementary particles in nonlinear quantum field The theory of soliton movement of superconductive features The soliton movements in condensed state systemsontents

Topological Solitons

Author: Nicholas S. Manton

Publisher:

Published: 2002-02

Total Pages: 493

ISBN-13: 9780521632447

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"This book is suitable for graduate students and researchers in theoretical physics and applied mathematics."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

Solitons

Author: S.E. Trullinger

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 916

ISBN-13: 0444598294

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In the twenty years since Zabusky and Kruskal coined the term ``soliton'', this concept changed the outlook on certain types of nonlinear phenomena and found its way into all branches of physics. The present volume deals with a great variety of applications of the new concept in condensed-matter physics, which is particularly reached in experimentally observable occurrences. The presentation is not centred around the mathematical aspects; the emphasis is on the physical nature of the nonlinear phenomena occurring in particular situations.With its emphasis on concrete, mostly experimentally verifiable cases, ``Solitons'' constitutes a very readable and instructive introduction to the subject as well as an up-to-date account of current developments in a field of research reaching maturity.

Variational Methods in Nonlinear Field Equations

Author: Vieri Benci

Publisher: Springer

Published: 2014-10-24

Total Pages: 271

ISBN-13: 3319069144

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The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.

Symmetry, Broken Symmetry, and Topology in Modern Physics

Author: Mike Guidry

Publisher: Cambridge University Press

Published: 2022-03-31

Total Pages: 666

ISBN-13: 1009008420

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Written for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincaré invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.