  We consider a coupled Wave-Klein-Gordon system in 3D, which is a simplified
model for the global nonlinear stability of the Minkowski space-time for
self-gravitating massive fields. In this paper we study the large-time
asymptotic behavior of solutions to such systems, and prove modified wave
operators for small and smooth data with mild decay at infinity. The key
novelty comes from a crucial observation that the asymptotic dynamics are
dictated by the resonant interactions. As a consequence, our main results
include the derivation of a resonant system with good error bounds, and a
detailed description of the asymptotic dynamics of such quasilinear evolution
system of hyperbolic and dispersive type.
