Elements of soliton theory and related concepts

The following sections are included:

• Introduction

• The Korteweg–de Vries soliton

• Topological solitons in (1 + 1)-d relativistic field theories

  • The sine-Gordon soliton

  • The λϕ⁴ kink

• Topological solitons in gauge theories

  • The Nielsen–Olesen vortex

  • The 't Hooft–Polyakov monopole

• Topological defect classification and the Kibble–Zurek mechanism for defect formation

  • Exact homotopy sequences

  • Topological defects in theories with SSB

• Derrick theorem and defect stability

• Bogomol'nyi bounds

• Non-topological solitons

• Instantons and their manifestations

  • Collective coordinates and fermionic zero modes

• Appendix S Bäcklund transformation for the sine-Gordon system

• Appendix T Elements of homotopy theory