Constructing K\"ahler-Ricci solitons from Sasaki-Einstein manifolds

We construct gradient K"ahler-Ricci solitons on Ricci-flat K"ahler cone manifolds and on line bundles over toric Fano manifolds. Certain shrinking and expanding solitons are pasted together to form eternal solutions of the Ricci flow. The method we employ is the Calabi ansatz over Sasaki-Einstein manifolds, and the results generalize constructions of Cao and Feldman-Ilmanen-Knopf.