3-WAVE RESONANT INTERACTION IN A THIN-LAYER

We analyze in detail conversion of a pump wave into two daughter waves (DWs) on an infinitely thin nonlinear layer, assuming that the conversion is initiated by weak seed pulses of the DWs. Three cases corresponding to different signs of the group velocities of the DWs are considered separately. In the case when both velocities are opposite to that of the pump wave, a threshold value of the ''strength'' of the nonlinear layer is found, above which oscillations between the conversion and the inverse process of recombination set in. In the case when the DW group velocities have different signs, the shapes of the generated DW pulses do not depend upon shapes of the corresponding ''seed'' pulses. In this case, multiple solutions are possible, provided the nonlinearity is strong enough.