  Spontaneous creation of solitons in quadratic media by the downconversion,
i.e., parametric instability against the generation of fundamental-frequency
excitations, from the truncated Airy-wave (AW) mode in the second-harmonic
component is studied. Parameter regions are identified for the generation of
one, two, and three solitons, with additional small-amplitude "jets". Shares of
the total power carried by individual solitons are found. Also considered are
soliton patterns generated by the downconversion from a pair of AWs bending in
opposite directions.
