Abstract
A translating soliton is a surface in Euclidean space $$\mathbb {R}^3$$ that is minimal for a log-linear density $$\phi (x,y,z)=\alpha x+\beta y+\gamma y$$ , where $$\alpha ,\beta ,\gamma $$ are real numbers not all zero. We characterize all translating solitons that are foliated by circles and the ones that are graphs of type $$z=f(x)+g(y)$$ .
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