Abstract
This paper is a review of results obtained by the authors in the field of non-linear monochromatic wave-particles interaction in the inhomogeneous plasma. The explicit expressions for the nonlinear growth rates and frequency shifts are derived and investigated for the cases of weak and strong inhomogeneity (the physical difference between the two cases is that in the first case there are trapped as well as untrapped particles; in the second one there are only untrapped particles). The modulational instability connected with the frequency shift, arising due to the nonlinearity and inhomogeneity, is considered.
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