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sine–gordon soliton

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20 - Kink Solutions in ϕ4 and Sine-Gordon, Domain Walls and Topology
from Part II - Solitons and Topology; Non-Abelian Theory
Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
Book:

Classical Field Theory

Published online:

04 March 2019

Print publication:

14 March 2019, pp 185-194
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Summary

We consider “kink” solutions of 1+1 dimensional scalar field models with a canonical kinetic term and a potential for the scalar. Classical, static, soliton solutions are found as solutions of the classical mechanics motion in an inverted (V = -U) potential. The cases of the $\phi^4$ and Higgs models are analyzed, and the Higgs “kink” solution is found and described. The sine–Gordon model is also analyzed and its soliton found. The topology of the solutions is characterized. Finally, embedding of the solution in higher dimensions as a “domain wall” is also considered.