Isospinning hopfions

Abstract

The problem of constructing internally rotating solitons of fixed angular frequency $\omega$ in the Faddeev-Skyrme model is reformulated as a variational problem for an energy-like functional, called pseudoenergy, which depends parametrically on $\omega$. This problem is solved numerically using a gradient descent method, without imposing any spatial symmetries on the solitons, and the dependence of the solitons' energy on $\omega$, and on their conserved total isospin $J$, studied. It is found that, generically, the shape of a soliton is independent of $\omega$, and that its size grows monotonically with $\omega$. A simple elastic rod model of time-dependent hopfions is developed which, despite having only one free parameter, accounts well for most of the numerical results.

21 pages. Published version. Note and reference added

References in corpus (5)

• Knots in the Skyrme-Faddeev model
• Massive Hopfions
• Classically Isospinning Hopf Solitons
• Hopf solitons and elastic rods
• Helical buckling of Skyrme-Faddeev solitons

Cited by in corpus (14)

• Torus knots as Hopfions
• Isospinning baby Skyrmion solutions
• Gravitating solitons and black holes with synchronised hair in the four dimensional O(3) sigma-model
• Classically isospinning Skyrmion solutions
• Gauged Baby Skyrme Model with Chern-Simons term
• Winding Hopfions on R^2 x S^1
• Isorotating Baby Skyrmions
• Oscillons in a perturbed signum-Gordon model
• Gauged Hopfions
• Toroidal domain walls as Hopfions
• Hopfions interaction from the viewpoint of the product ansatz
• Solitons in the Gauged Skyrme-Maxwell Model
• Magnetic Hopfions in the Faddeev-Skyrme-Maxwell model
• Isospinning Skyrmions