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
StatePublished - 1996

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Sigma Models
Necessary Conditions
Vortex
Sufficient Conditions
Magnetic Field
vortices
Open interval
Nonlinear Elliptic Equations
Source Terms
Natural number
Decay Rate
magnetic fields
decay rates
magnetic flux
field strength
Gauge
Lower bound
If and only if
intervals
Configuration

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

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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.",
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