The non-linear interaction of a few coherent, weakly damped longitudinal and transverse waves in an unmagnetized plasma is considered by means of the coupled mode theory. Using the equations describing the non-linear wave interactions the threshold electric fields and initial growth rates of a number of parametric instabilities are calculated. The following four instabilities, all of which are relevant to laser fusion are considered: (i) the parametric ion-acoustic-Langmuir wave integration, (ii) the two plasmon decay, (iii) stimulated Raman scattering and (iv) stimulated Brillouin scattering. All these instabilities are driven by a large amplitude electro-magnetic wave.