On the kinetics of high- and low-frequency waves in nonlinear media

The kinetics of weak turbulence in a nonlinear medium is considered in which there are two types of interacting waves, low and high frequency. The stationary Kolmogorov spectra are found which correspond to constant fluxes over the integral of motion spectrum, i.e. the energy and number of high frequency quasiparticles. Two cases are considered, that of identical indexes for the dispersion laws of high and low frequency waves and the case of the ''differential approximation'' when the change in energy of the high frequency waves in each scattering act is small. The locality conditions for the Kolmogorov spectra are found. The results are applied to the problem of interaction between Langmuir and ion-sound waves in a plasma