Consider, in dimension 3, a system of coupled Klein-Gordon equations with
different speeds, and an arbitrary quadratic nonlinearity. We show, for data
which are small, smooth, and localized, that a global solution exists, and that
it scatters. The proof relies on the space-time resonance approach; it turns
out that the resonant structure of this equation has features which were not
studied before, but which are generic in some sense.Comment: 35 page
