The Faddeev knots as stable solitons: Existence theorems

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The problem of existence of knot-like solitons as the energy-minimizing configurations in the Faddeev model, topologically characterized by Hopf invariant, Q, is considered. It is proved that, in the full space situation, there exists an infinite set S of integers so that for any m ∈ S, the Faddeev energy, E, has a minimizer among the class Q = m; in the bounded domain situation, the same existence theorem holds when S is the set of all integers. One of the important technical results is that E and Q satisfy the sublinear inequality E ≤ C|Q|3/4, where C > 0 is a universal constant, which explains why knotted (clustered soliton) configurations are preferred over widely separated unknotted (multisoliton) configurations when |Q| is sufficiently large.

Original languageEnglish (US)
Pages (from-to)187-197
Number of pages11
JournalScience in China, Series A: Mathematics
Issue number2
StatePublished - Apr 2004


  • Hopf invariant
  • Knots
  • Minimization
  • Solitons

ASJC Scopus subject areas

  • General Mathematics


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