Antiperiodic solitons of the Goldstone model on S^1

Our purpose is to present all static solutions of the Goldstone model on a circle in 1+1 dimensions with an antiperiodicity condition imposed on the scalar fields. Jacobi elliptic and standard trigonometric functions are used to express the solutions found and stability analysis of the latter is what follows. Classically stable quasi-topological solitons are identified.