Topological and non-topological solitons in scalar field theories


Topological and non-topological solitons in scalar field theories

Yakov M. Shnir

(Cambridge monographs on mathematical physics)

Cambridge University Press, 2018

  • : hardback

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Includes bibliographical references(p. [247]-263) and index



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.


  • Preface
  • Part I. Kinks and Solitary Waves: 1. Sine-Gordon model
  • 2. Kinks in the models with polynomial potentials
  • 3. Non-topological solitons: Korteweg-de-Vries system
  • Part II. O(3) Sigma Model, Lumps and Baby Skyrmions: 4. O(3) Non-linear sigma model
  • 5. Baby skyrmions
  • Part III. Q-balls, Skyrmions and Hopfions: 6. Q-balls
  • 7. Skyrmions
  • 8. Hopfions
  • References
  • Index.

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