A necessary and sufficient condition for the existence of multisolitons in a self-dual gauged sigma model

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Abstract

This paper presents a resolution of the gauged O(3) sigma model proposed by B.J. Schroers in which the matter field φ maps R2 into S2 while the vector gauge potential gives rise to a magnetic field. It is shown that for each natural number N there are solutions to saturate the classical energy lower bound E ≧ 4πN for the field configurations in the topological family deg(φ) = N if and only if N ≠ 1. Furthermore the solutions obtained depend on at least 4N - 3 continuous parameters, the associated magnetic flux can assume its value in an open interval, and the decay rates of the field strengths may be specified in a suitable range. These solutions are multisolitons represented by N prescribed lumps of the magnetic field, simulating N identical particles in equilibrium, and are governed by a nonlinear elliptic equation with both vortex and anti-vortex source terms.

Original languageEnglish (US)
Pages (from-to)485-506
Number of pages22
JournalCommunications In Mathematical Physics
Volume181
Issue number2
DOIs
StatePublished - Jan 1 1996

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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