  Nonlinear sigma models compatible with the aratyn-Ferreira-Zimerman ansatz
are discussed, the latter ansatz automatically leading to configurations with
definite values of the Hopf index. These models are allowed to involve a weight
factor which is a function of one of the toroidal coordinates. Depending on the
choice of the weight factor, the field equation takes various forms. In one
model with a special weight factor, the field equation turns out to be the
fifth Painleve equation. This model suggests the existence of a knot soliton
strictly confined in a finite spatial volume. Some other interesting cases are
also discussed.
