Shota Rustaveli National Science Foundation of GeorgiaStart Date: 2017-12-20 End Date: 2021-05-30
Theoretical and numerical investigation of nonlinear dynamics of collisional and collisionless interaction of the soliton and vortex type smultiscale structures in complex continuous media, including ionosphere and magnetosphere plasma, represents a big step prior in the theory of nonlinear wave processes. Such structures are observed in the near Earth space, in the atmosphere, hydrosphere and other media. Such studies establishes the close connections between the results of theoretical and experimental investigations of artificial impact on the plasma media in laboratory conditions and satellite observations of the earth ionosphere and magnetosphere, the possibilities of adequate interpretation of formation of the stable wave processes and structure decay with turbulization of the wave field and effects of transfer to the chaotic regimes.Besides, the results of theoretical and theoretical-modeler investigations will find natural application in stable stratified (fold) media with shear flows, which is important problem in the physics and hydrodynamics of atmosphere and plasma. Multiscale approach with consideration of all processes and phenomena, which take place in certain complex physical media (dispersed, dissipative, with different type instabilities) gives possibility for better and adequate description of in-situ observed nonlinear wave (also vortex) dynamics. On the basis of theoretical analysis and numerical experiments the soliton and vortex type (which cause solitary connected n-soliton and n-vortex systems in plasma and other complex continuous media, such as atmosphere, hydrosphere) local stationary state formation processes and conditions will be studied. In the framework of the project the problems of their interaction and decay, which is accompanied with energy radiation of considered physical system. For numerical experiments elaboration of a new codes and generalization of existing ones for numerical integration of the appropriate multiscale nonlinear integro-differential equations and dynamic systems is planned. These new approaches and methods will be elaborated with help of the foreign consultant and are based on his methodology. Proposed method is based on finite-difference schemes as well as on the dynamic spectral approaches, which is effective for minimization of the time costs.