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

Toroidal Spiral Strings in Higher-dimensional Spacetime