On the existence of multivortices in a generalized Bogomol'nyi system

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Abstract

An interesting feature of the generalized Abelian Higgs vortex model introduced by M. Lohe is that it allows a wider class of Higgs self-interaction potential functions, yet, noninteracting multivortices are still present in the critical coupling phase as the solutions of a modified Bogomol'nyi system. In this paper, we add two new classes of multivortex solutions to Lohe's model. We prove that, under the 't Hooft boundary condition, there are solutions realizing a periodic lattice structure and a quantized flux. A necessary and sufficient condition is obtained for the existence of such solutions. We also show that the Meissner effect occurs in the model. Moreover, we establish for any given vortex distribution in the plane, the existence of a one-parameter family of gauge-distinct solutions of infinite energy.

Original languageEnglish (US)
Pages (from-to)677-696
Number of pages20
JournalZAMP Zeitschrift für angewandte Mathematik und Physik
Volume43
Issue number4
DOIs
StatePublished - Jul 1992

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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