We show experimentally and theoretically that cascading due to two-wave par
ametric frequency conversion in quadratic materials acts as an effective fo
cusing or defocusing nonlinearity, depending not only on, mismatch, but als
o on, the selected wave, and the dominant type of process (second-harmonic
generation or down-conversion). A dramatic asymmetry of beam spreading and
threshold lowering for soliton formation against mismatch is, the clear exp
erimental signature of this behavior.