  We present new experimental results on the transition from the coherent-phase
to the random-phase three-wave interactions in capillary waves under parametric
excitation. Above the excitation threshold, coherent wave harmonics spectrally
broaden. An increase in the pumping amplitude increases spectral widths of wave
harmonics and eventually causes a strong decrease in the degree of the
three-wave phase coupling. The results point to the modulation instability of
capillary waves, which leads to breaking of continuous waves into ensembles of
short-lived wavelets or envelope solitons, as the reason for the phase
randomization of three-wave interactions.
