Topological and Non-Topological Solitons in Scalar Field Theories

Yakov M. Shnir

doi:10.1017/9781108555623

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.

'Structured in three parts, this book provides a comprehensive introduction to the description and construction of solitons in various models. In the first two chapters of part one, the author discusses the properties of topological solitons in the completely integrable [s]ine-Gordon model and in the non-integrable models with polynomial potentials. Then, in chapter three, he introduces solitary wave solutions of the Korteweg–de Vries equation … Part two deals with higher dimensional nonlinear theories. … Part three focuses mainly on the solitons in three spatial dimensions. … Based on the author’s lecture notes for a graduate-level course, this book is addressed at graduate students in theoretical physics and mathematics, as well as researchers interested in solitons.'

Virginia Greco Source: CERN Courier

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Topological and Non-Topological Solitons in Scalar Field Theories

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Contents

Frontmatter
pp i-vi

Dedication
pp vii-viii

Contents
pp ix-x

Preface
pp xi-xiv

Part I - Kinks and Solitary Waves
pp 1-2

Chapter 1 - Sine-Gordon Model
pp 3-32

Chapter 2 - Kinks in Models with Polynomial Potentials in (1 + 1) Dimensions
pp 33-60

Chapter 3 - Non-Topological Solitons: The Korteweg–de Vries System
pp 61-84

Part II - O(3) Sigma Model, Lumps, and Baby Skyrmions
pp 85-86

Chapter 4 - O(3) Nonlinear Sigma Model
pp 87-112

Chapter 5 - Baby Skyrmions
pp 113-136

Part III - Q-Balls, Skyrmions, and Hopfions
pp 137-138

Chapter 6 - Q-Balls
pp 139-170

Chapter 7 - Skyrmions
pp 171-220

Chapter 8 - Hopfions
pp 221-246

Bibliography
pp 247-263

Index
pp 264-266

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