  The purpose of this paper is to introduce the Ricci Yang-Mills soliton
equations on nilpotent Lie groups. In the 2-step nilpotent setting, we show
that these equations are strictly weaker than the Ricci soliton equations.
Using techniques from Geometric Invariant Theory, we develop a procedure to
build many different kinds of Ricci Yang-Mills solitons. We finish this note by
producing examples of Lie groups that do not admit Ricci soliton metrics but
that do admit Ricci Yang-Mills soliton metrics.
