The Faddeev knots as stable solitons: Existence theorems

Research output: Contribution to journalArticle

Abstract

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
Volume47
Issue number2
StatePublished - Apr 2004

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Existence Theorem
Knot
Solitons
Configuration
Hopf Invariant
Integer
Energy
Minimizer
Bounded Domain
Model
Class

Keywords

  • Hopf invariant
  • Knots
  • Minimization
  • Solitons

ASJC Scopus subject areas

  • General

Cite this

The Faddeev knots as stable solitons : Existence theorems. / Lin, Fanghua; Yang, Yisong.

In: Science in China, Series A: Mathematics, Vol. 47, No. 2, 04.2004, p. 187-197.

Research output: Contribution to journalArticle

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