Hopf solitons in modern mathematical physics


The first works

[A.M. Kamchatnov "Topological solitons in magnetohydrodynamics", Sov. Phvs. JETP 55, 69 (1982) ref, arXiv:physics/0409093v1]. The author has found exact solution of the equations of magnetohydrodynamics which describes soliton with Hopf index = 1.

A detailed description will be added

The results of recent years

Simulations of Hopf fibration-like configuration of plasma confinement presented in [C.B. Smiet, S. Candelaresi, A. Thompson, J. Swearngin, J. W. Dalhuisen, D. Bouwmeester "Self-Organizing Knotted Magnetic Structures in Plasma", arXiv:1507.08780v1, Phys. Rev. Lett. 115, 095001 (2015) ref], [C.B. Smiet, S. Candelaresi, D. Bouwmeester "Ideal relaxation of the Hopf fibration", arXiv:1610.04719v1, Physics of Plasmas 24, 072110 (2017) ref]

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