  We employ the generic three-wave system, with the $\chi ^{(2)}$ interaction
between two components of the fundamental-frequency (FF) wave and
second-harmonic (SH) one, to consider collisions of truncated Airy waves (TAWs)
and three-wave solitons in a setting which is not available in other nonlinear
systems. The advantage is that the single-wave TAWs, carried by either one of
the FF component, are not distorted by the nonlinearity and are stable,
three-wave solitons being stable too in the same system. The collision between
mutually symmetric TAWs, carried by the different FF components, transforms
them into a set of solitons, the number of which decreases with the increase of
the total power. The TAW absorbs an incident small-power soliton, and a
high-power soliton absorbs the TAW. Between these limits, the collision with an
incident soliton converts the TAW into two solitons, with a remnant of the TAW
attached to one of them, or leads to formation of a complex TAW-soliton bound
state. At large velocities, the collisions become quasi-elastic.
