Excitation of nonlinear acoustic oscillations in moving inhomogeneous plasma. Equations for the interacting-wave amplitudes

A dynamic system of equations is formulated for the amplitudes of standing acoustic waves excited in inhomogeneous plasma flows in channels. This system is intended for the analysis and calculation of the nonlinear stage in the development of acoustic instability in sufficiently dense moving weakly ionized plasma, in the presence of volume electromagnetic perturbations. Equations are obtained for the complex amplitudes describing the near-resonant interaction of twodimensional acoustic modes localized between two cutoff cross sections. These equations take account of the energy exchange between growing and damping modes, as well as the frequency detuning from synchronism in three-wave interactions.