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Let $(M, g, f, J, \lambda)$ be a complete K\"{a}hler gradient Ricci soliton.Our first theorem classifies such a structure in real dimension four when $f$has a geodesic gradient, a notion weaker than isoparametric. The soliton mustbe either a product metric or of cohomogeneity one with deformed homogeneousSasakian orbits. The second result is a partially reverse statement in anydimension. Suppose that each regular level set of $f$ is a deformed contactmetric structure then the soliton is totally determined by a regular Sasakianmodel, which is a Riemannian submersion, with circle fibers, over aK\"{a}hler-Einstein manifold. In particular, $f$ must be isoparametric. Animportant ingredient of the proof is a characterization of a deformed Sasakianstructure which generalizes a classical result.

K\"{a}hler Solitons, Contact Structures, and Isoparametric Functions