Rotational $K^{\alpha}$-translators in Minkowski Space

A spacelike surface in Minkowski space $\mathbb{R}_1^3$ is called a $K^{\alpha}$-translator of the flow by powers Gauss curvature if satisfies $K^{\alpha} = \langle N, \vec{v} \rangle$, $\alpha \neq 0$, where $K$ curvature, $N$ unit normal vector field and $\vec{v}$ direction $\mathbb{R}_1^3$. In this paper, we classify all rotational $K^{\alpha}$-translators. This classification will depend on causal character rotation axis. Although theory $K^{\alpha}$-flow holds for surfaces, equation describing $K^{\alpha}$-translators still valid timelike surfaces. So also investigate surfaces that satisfy same prescribing equation.