The Goldstone model static solutions on S^1
  We study in a systematic way all static solutions of the Goldstone model in 1+1 dimension with a periodicity condition on the spatial coordinate. The solutions are presented in terms of the standard trigonometric functions and of Jacobi elliptic functions. Their stability analysis is carried out, and the complete list of classical stable quasi-topological solitons is given. 
Y. Brihaye, T. N. Tomaras