Investigation of linear and nonlinear mode conversions in inhomogeneous plasma and finding of new effects of the principal importance including the following:

• the possibility of 100 % linear mode conversion;

• the higher harmonics generation under the electromagnetic wave interactions with the inhomogeneous plasma in the plasma resonance layers presence (together with V.E.Zakharov, N.S.Erokhin); this effect was confirmed experimentally and it is important, in particular, for a plasma diagnostics;

• the analysis of electromagnetic wave beams self-focusing in the inhomogeneous plasma and their passage into the overdense plasma region (together with R.Z.Sagdeev, V.V.Mukhin, N.S.Erokhin, V.E.Novikov); this phenomenon is important for the overdense plasma heating by powerful electromagnetic radiation and for nonlinear transillumination of the thick opaque plasma layers;

• studyings of the kinetic nonlocal effects arising at the electromagnetic wave interactions with inhomogeneous plasma and the discovery of thick wave barrier effective transillumination, conditioned by the phase focusing of charged particle microbeams, which was confirmed experimentally (together with A.A.Vodyanitsky, N.S.Erokhin, V.N.Oraevsky, V.I.Muratov et.al).