On the theory of nonlinear interactions of waves in a plasma in the presence of strong variable electric field

Equations for the coherent nonlinear interactions of three (four) waves or their beat waves with the pumping wave are obtained on the basis of the nonlinear equation for the Fourier transform of the oscillation electrostatic potential which accounts for finite displacements of particles in the pumping wave field. The equations are shown to possess the energy and momentum conservation laws and the Manley-Rowe relations for these equations are fulfilled. The system of equations describing the three-wave interactions in the random phase approximation and accounting for the finite displacements of particles in the pumping wave field is also shown to possess the energy and momentum conservation laws