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Solitons emerge in various nonlinear systems – from nonlinear optics and condensed matter to nuclear physics, cosmology, and supersymmetric theories – as stable, localized configurations behaving in many ways like particles. This book provides an introduction to integrable and non-integrable scalar field models with topological and non-topological soliton solutions. It brings together discussion of solitary waves and construction of soliton solutions in various models and provides a discussion of solitons using simple model examples, including the Kortenweg–de Vries system, the sine-Gordon model, kinks, oscillons, skyrmions, and hopfions. The classical field theory of the scalar field in various spatial dimensions is used throughout to present related concepts, at technical and conceptual levels. 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