Plasma kinetics (1955), ionosphere physics (1955), nonlinear dynamics
of noncollisional plasma (1963), nonlinear waves in dispersive hydrodynamics
(1973), artificial ionized layers in atmosphere (1977),
electrodynamics of neutron star magnetosphere (19831993),
nonlinear dynamics of dark matter (1988).
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 (Eregion) and upper (Fregion) Ionosphere,
resonance instability, nonlinear theory of stationary striations,
transport properties in the Ionosphere, turbulence in the ionospheric
Eregion, aerodynamic flows around bodies (artificial satellites, rockets) in rarefied plasma,
electrodynamics of ionospheric  magnetospheric current system,
and longrange 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).
The current interests:
microlensing and its connection with cold dark matter particles, runaway breakdown and
lightening initiation, nonlinear theory of stationary striations, statistical limit for
nonlinear dispersive waves dynamics at fully determined initial conditions ("dynamical
soliton turbulence"), ionospheric turbulence,
artificial ozone layers.
