NON-LINEAR WAVE-WAVE INTERACTIONS WITHOUT RESONANCE CONDITIONS

Third-order nonlinear wave-wave interactions are possible without any resonance conditions which link frequencies and wave-vectors of the interacting waves. Usually, but not always, interactions without resonances result in a mere frequency shift. Some models, however, involve changes in the amplitudes as well. This is illustrated on several examples of the self-modulation of one wave, firstly in general terms, then for a model equation in a dissipative medium, and finally for an electrostatic wave in a medium with various nonlinear conductivities. Depending upon the medium, three cases are possible: either the wave amplitude does not change, or the wave dissipates its energy into the medium, or the medium feeds an explosive instability.