  The Aratyn-Ferreira-Zimerman (AFZ) model is a conformal field theory in
three-dimensional space. It has solutions that are topological solitons
classified by an integer-valued Hopf index. There exist infinitely many axial
solutions which have been found analytically. Axial, knot and linked solitons
are found numerically to be static solutions using a modified volume preserving
flow for Hopf index one to eight, allowing for comparison with other Hopf
soliton models. Solutions include a static trefoil knot at Hopf index five. A
one-parameter family of conformal Skyrme-Faddeev (CSF) models, consisting of
linear combinations of the Nicole and AFZ models, are also investigated
numerically. The transition of solutions for Hopf index four is mapped across
these models. A topological change between linked and axial solutions occurs,
with fewer models permitting axial solitons than linked solitons at Hopf index
four.
