Nonlinear interaction of wave packets

We study the frequency shift suffered by a wave packet propagating in a homogeneous and stationary plasma, when subjected to the influence of a second wave packet which nonlinearly changes the dielectric properties of the plasma. The opposite cases of an adiabatic frequency shift and a relativistic Doppler shift are discussed in detail. The contribution of the inverse Faraday effect to the adiabatic situation is also taken into account. The results might be relevant in the search for new generators in the sub-millimetre ranges and for the understanding of spectral transfers of energy in a plasma.