1. Theory, mathematical modeling and computer simulation of evolution, stability and dynamics of interaction of multidimensional nonlinear wave structures of soliton and vortex types in a plasma and other media with dispersion;

2. Applications of nonlinear wave theory to the dynamics of nonlinear waves and solitons propagating in the atmosphere, hydrosphere, ionosphere and magnetosphere from the sources of pulse type (such as the seismic phenomena, strong explosions, solar terminator, solar eclipces etc.); study of influence of the wave ionospheric structures on luctuations of the radiosignals in the wide frequency range;

3. Mathematical modeling of the electromagnetic fields excited by the elements of the electrical powersystems, and influence of the external EM fields on these elements.