  The Skyrme-Faddeev model is a modified sigma model in three-dimensional
space, which has string-like topological solitons classified by the
integer-valued Hopf charge. Numerical simulations are performed to compute
soliton solutions for Hopf charges up to sixteen, with initial conditions
provided by families of rational maps from the three-sphere into the complex
projective line. A large number of new solutions are presented, including a
variety of torus knots for a range of Hopf charges. Often these knots are only
local energy minima, with the global minimum being a linked solution, but for
some values of the Hopf charge they are good candidates for the global minimum
energy solution. The computed energies are in agreement with Ward's conjectured
energy bound.
