The nonlinear dynamics of localized selforganized structures in plasmas, nano-composite meterials, liquid and fotonic crystals, and ultracold condensates

Theoretical and numerical studies of the generation, propagation and temporal stability of the spatial and spatio-temporal dissipative solitons in semiconductors, nanocomposites, photon crystals, metamaterials, atmosphere and biological environments. Nonlinear phenomena in the plasma of the Earth's ionosphere and magnetosphere, in magnetically confined and laser generated fusion plasmas, in ultracold quantum plasma and in metal vapor condensates. Attaining conditions for the controlled fusion in tokamaks by reducing the anomalous transport in the edge and eliminating the undesired effects of dust. Development of diagnostic methods for nonequillibrium laboratory plasmas, used in the treatment of surfaces, consisting of multilayer dielectric and/or semiconductor films. The diagnostics and control will enable the determination of the degree of surface modification without interrupting the discharge. The study of the propagation and dynamics of self-organized optical structures – solitons, light packets and vortices in nonlineran, nonlocal optical media. Of particular interest are counterpropagating laser beams, because of their inherent capability for two-way data transmission. Effects of the surfaces on the propagation of laser light in photonic- and liquid crystals. Study of copropagating and counterpropagating surface waves in multidimensional composite materials. Solving multidimensional PDEs of nonlinear optics and Bose-Einstein condensates and testing the stability.