  Ricci-like solitons on Sasaki-like almost contact B-metric manifolds are the
object of study. Cases, where the potential of the Ricci-like soliton is the
Reeb vector field or pointwise collinear to it, are considered. In the former
case, the properties for a parallel or recurrent Ricci-tensor are studied. In
the latter case, it is shown that the potential of the considered Ricci-like
soliton has a constant length and the manifold is $\eta$-Einstein. Other
curvature conditions are also found, which imply that the main metric is
Einstein. After that, some results are obtained for a parallel symmetric
second-order covariant tensor on the manifolds under study. Finally, an
explicit example of dimension 5 is given and some of the results are
illustrated.
