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The Faddeev knots as stable solitons: Existence theorems

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Abstract

The problem of existence of knot-like solitons as the energy-minimizing configurations in the Faddeev model, topologically characterized by an 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.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 10012, New York, New York, U S A

    Fanghua Lin

  2. School of Mathematics, Institute for Advanced Study, 08540, Princeton, New Jersey, U S A

    Yisong Yang

  3. Department of Mathematics, Polytechnic University, 11201, Brooklyn, New York, U S A

    Yisong Yang

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  1. Fanghua Lin
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  2. Yisong Yang
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Correspondence to Fanghua Lin or Yisong Yang.

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Lin, F., Yang, Y. The Faddeev knots as stable solitons: Existence theorems. Sci. China Ser. A-Math. 47, 187–197 (2004). https://doi.org/10.1360/02ys0351

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