The main results:
Plasma kinetics: theory of collisional plasmas, overheat instability, theory of runaway electrons, runaway breakdown, turbulent transport in plasma.
Ionospheric physics: nonlinear phenomena induced by powerful radio waves in lower (E-region) and upper (F-region) Ionosphere, resonance instability, nonlinear theory of stationary striations, transport properties in the Ionosphere, turbulence in the ionospheric E-region, aerodynamic flows around bodies (artificial satellites, rockets) in rarefied plasma, electrodynamics of ionospheric - magnetospheric current system, and long-range propagation of short radio waves in the Ionosphere.
Atmospheric physics: creation of artificial ionized layers by powerful radio waves, artificial ozone layers, runaway breakdown of air, and high altitude lightening.
Nonlinear dynamics and nonlinear waves: expanding of a plasma into vacuum, singular limits for quasiclassical solution of partial differential equations (Gurevich - Pitaevsky problem), theory of nondissipative shock waves, multisoliton structure, and 2D flow around thin bodies in dispersive hydrodynamics, shock waves in a weakly dissipative hydrodynamics, statistical limit for fully integrable system.
Astrophysics: theory of radio pulsar magnetosphere and the theory of pulsar radio emission (with V.S.Beskin and Ya.N.Istomin), nonlinear dynamics of Jeans instability in nondissipative matter, universal scaling low, hierarchical structures (with K.P.Zybin).