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Knots as Stable Soliton Solutions in a Three-Dimensional Classical Field Theory
Open accessAbstract
We examine in detail recent claims that knotlike structures exist in a simple classical field theory which are stabilized by the Hopf charge. We present minimum energy configurations for charges one to eight generated numerically. It is found that the solutions exhibit a spectacular variety of behavior including closed loops, linked loops, and, most interestingly, knots.
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Cited by
Dennis, M. R., King, R. P., Jack, B., O’Holleran, K., & Padgett, M. J. (2010) · Nature Physics · doi:10.1038/nphys1504 · Cited by 486
Ackerman, P. J., & Smalyukh, I. I. (2017) · Physical Review X · doi:10.1103/physrevx.7.011006 · Cited by 126
Ward, R. S. (1999) · Nonlinearity · doi:10.1088/0951-7715/12/2/005 · Cited by 76
Optical second-order skyrmionic hopfion
Ehrmanntraut, D., Droop, R., Sugic, D., Otte, E., Dennis, M. R., & Denz, C. (2023) · Optica · doi:10.1364/optica.487989 · Cited by 43
Optical excitations of Skyrmions, knotted solitons, and defects in atoms
Parmee, C. D., Dennis, M. R., & Ruostekoski, J. (2022) · Communications Physics · doi:10.1038/s42005-022-00829-y · Cited by 40
Metadata
- Authors
- Battye, R. A., & Sutcliffe, P. M.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1998-11-30
- Volume
- 81
- Issue
- 22
- Pages
- 4798-4801
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1885649463
- Cited by
- 285
- References
- 0
- FWCI
- 9.66
- Type
- journal article
- Language
- en
- Open access
- green
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- CoChat. (2026). Citation check: Knots as Stable Soliton Solutions in a Three-Dimensional Classical Field Theory. https://app.cochat.ai/papers/10.1103/physrevlett.81.4798
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- Battye, R. A., & Sutcliffe, P. M. (1998). Knots as Stable Soliton Solutions in a Three-Dimensional Classical Field Theory. Physical Review Letters. https://doi.org/10.1103/physrevlett.81.4798
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
