  We study the issue of stability of static soliton-like solutions in some
non-linear field theories which allow for knotted field configurations.
Concretely, we investigate the AFZ model, based on a Lagrangian quartic in
first derivatives with infinitely many conserved currents, for which infinitely
many soliton solutions are known analytically. For this model we find that
sectors with different (integer) topological charge (Hopf index) are not
separated by an infinite energy barrier. Further, if variations which change
the topological charge are allowed, then the static solutions are not even
critical points of the energy functional. We also explain why soliton solutions
can exist at all, in spite of these facts. In addition, we briefly discuss the
Nicole model, which is based on a sigma-model type Lagrangian. For the Nicole
model we find that different topological sectors are separated by an infinite
energy barrier.
