Translators of flows by powers of the Gauss curvature

A K-alpha-translator is a surface in Euclidean space R-3 that moves by translations in a spatial direction under the K-alpha-flow, where K is the Gauss curvature and alpha is a constant. We classify all K-alpha-translators that are rotationally symmetric. In particular, we prove that for each alpha there is a K-alpha-translator intersecting orthogonally the rotation axis. We also describe all K-alpha-translators invariant by a uniparametric group of helicoidal motions and the translators obtained by separation of variables.