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Hopf solitons in the Nicole model

Gillard, M.; Sutcliffe, P.M.

Hopf solitons in the Nicole model Thumbnail


M. Gillard


The Nicole model is a conformal field theory in a three-dimensional space. It has topological soliton solutions classified by the integer-valued Hopf charge, and all currently known solitons are axially symmetric. A volume-preserving flow is used to construct soliton solutions numerically for all Hopf charges from 1 to 8. It is found that the known axially symmetric solutions are unstable for Hopf charges greater than 2 and new lower energy solutions are obtained that include knots and links. A comparison with the Skyrme–Faddeev model suggests many universal features, though there are some differences in the link types obtained in the two theories.


Gillard, M., & Sutcliffe, P. (2010). Hopf solitons in the Nicole model. Journal of Mathematical Physics, 51(12), Article 122305.

Journal Article Type Article
Publication Date Dec 1, 2010
Deposit Date Feb 3, 2011
Publicly Available Date Oct 9, 2012
Journal Journal of Mathematical Physics
Print ISSN 0022-2488
Electronic ISSN 1089-7658
Publisher American Institute of Physics
Peer Reviewed Peer Reviewed
Volume 51
Issue 12
Article Number 122305
Keywords Conformal field theory, Skyrmions, Topology.


Published Journal Article (180 Kb)

Copyright Statement
Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Gillard, M. and Sutcliffe, P.M. (2010) 'Hopf solitons in the Nicole model.', Journal of mathematical physics., 51 (12). p. 122305 and may be found at

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