### Abstract

In this paper we construct static cosmic string solutions in the Bogomol'nyi phase of the Abelian Higgs model in an S2 setting. The strings are located at the north and south poles and have identical winding numbers. This construction, in particular, solves an open problem regarding the existence of a 2-string solution on S2. Furthermore, we prove that there are no symmetric solutions realizing N strings superimposed at a single point. Such a result implies, in particular, that there is no symmetric 1-string solution on S2 and is the only known non-existence theorem for cosmic strings confined on a compact surface. The symmetry of the underlying system enables us to work on a nonlinear ordinary differential equation subject to some prescribed boundary data at t = ±00. A shooting method is employed as an analytic tool in the study of the existence problem.

Original language | English (US) |
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Pages (from-to) | 581-591 |

Number of pages | 11 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 453 |

Issue number | 1958 |

DOIs | |

State | Published - Jan 1 1997 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)