摘要
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|<sup>3/4</sup>, 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.
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.
作者
LIN Fanghua & YANG YisongCourant Institute of Mathematical Sciences, New York University, New York, New York 10012, U. S. A.School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, U. S. A.
Department of Mathematics, Polytechnic University, Brooklyn, New York 11201, U. S. A.
