### 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 language | English (US) |
---|---|

Pages (from-to) | 187-197 |

Number of pages | 11 |

Journal | Science in China, Series A: Mathematics |

Volume | 47 |

Issue number | 2 |

State | Published - Apr 2004 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Science in China, Series A: Mathematics*, vol. 47, no. 2, pp. 187-197.

}

TY - JOUR

T1 - The Faddeev knots as stable solitons

T2 - Existence theorems

AU - Lin, Fanghua

AU - Yang, Yisong

PY - 2004/4

Y1 - 2004/4

N2 - 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.

AB - 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.

KW - Hopf invariant

KW - Knots

KW - Minimization

KW - Solitons

UR - http://www.scopus.com/inward/record.url?scp=3142699945&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3142699945&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:3142699945

VL - 47

SP - 187

EP - 197

JO - Science in China, Series A: Mathematics

JF - Science in China, Series A: Mathematics

SN - 1006-9283

IS - 2

ER -