The Goldstone model static solutions on S1

We study in a systematic way all static solutions of the Goldstone model in 1 + 1 dimensions with a periodicity condition imposed on the spatial coordinate. The solutions are presented in terms of standard trigonometric functions and of Jacobi elliptic functions. Their stability analysis is carried out, and the complete list of classically stable quasi-topological solitons is given. AMS classification scheme number: 12B90