  We report on our progress in research of separability of the Nambu-Goto
equation for test strings with a symmetric configuration in a shape of toroidal
spiral in a five-dimensional Kerr-AdS black hole. In particular, for a Hopf
loop string which is a special class of the toroidal spirals, we show the
complete separation of variables occurs in two cases, Kerr background and
Kerr-AdS background with equal angular momenta. We also obtain the dynamical
solution for the Hopf loop around a black hole and for the general toroidal
spiral in Minkowski background.
