  We describe the dynamics of magnetic skyrmions in synthetic antiferromagnets
(SAF), with a finite interlayer coupling. Due to the opposite gyrovector of the
skyrmions in the two SAF layers, the coupled skyrmions reach a stationary
regime with a spatial separation, in a direction orthogonal to their velocity.
As a consequence, and contrary to the ferromagnetic situation, a transient
regime necessarily occurs, with a finite acceleration, related to an inertia,
and that limits its time response. The formalism developed here, based on two
coupled Thiele equations, allows a quantitative description of this phenomenon.
The time constant associated to the transient regime scales inversely with the
antiferromagnetic coupling constant. We also show that the coupling force
reaches a maximal value at a finite skyrmion separation. This sets a maximum
velocity limit, beyond which the the coupling force cannot stabilize the bound
state.
