  We study translating soliton solutions to the flow by powers of the curvature
of curves in the plane. We characterize these solitons as critical curves for
functionals depending on the curvature. More precisely, translating solitons to
the flow by powers of the curvature are shown to be generalized elastic curves.
In particular, focusing on the curve shortening flow, we deduce a new
variational characterization of the grim reaper curve.
