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 conver sion is initiated by weak seed pulses of the DWs. Three cases correspo nding to different signs of the group velocities of the DWs are consid ered separately. In the case when both velocities are opposite to that of the pump wave, a threshold value of the ''strength'' of the nonlin ear layer is found, above which oscillations between the conversion an d 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 nonlinea rity is strong enough.