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Hopf solitons on compact manifolds.

Ward, R.S. (2018) 'Hopf solitons on compact manifolds.', Journal of mathematical physics., 59 (2). 022904.


Hopf solitons in the Skyrme-Faddeev system on R3 typically have a complicated structure, in particular when the Hopf number Q is large. By contrast, if we work on a compact 3-manifold M, and the energy functional consists only of the Skyrme term (the strong-coupling limit), then the picture simplifies. There is a topological lower bound E ≥ Q on the energy, and the local minima of E can look simple even for large Q. The aim here is to describe and investigate some of these solutions, when M is S3, T3, or S2 × S1. In addition, we review the more elementary baby-Skyrme system, with M being S2 or T2.

Item Type:Article
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Publisher statement:© 2018 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 Ward, R.S. (2018). Hopf solitons on compact manifolds. Journal of Mathematical Physics 59(2): 022904 and may be found at
Date accepted:01 February 2018
Date deposited:07 February 2018
Date of first online publication:20 February 2018
Date first made open access:20 February 2019

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