Dynamics of Multidimensional Wave Structures of The Soliton and Vortex Types in Complex Continuous Media Including Atmosphere, Hydrosphere and Space Plasma

Abstract

The results of theoretical and numerical study of the structure and dynamics of 2D and 3D solitons and nonlinear waves described by Kadomtsev-Petviashvili, 3-DNLS classes of equations and also the vortex systems described by Euler-type equations are presented. The generalizations (relevant to various complex physical media), accounting for high-order dispersion corrections, dissipation, instabilities, and stochastic fluctuations of the wave fields are considered. Special attention is paid to the applications of the theory in different fields of modern physics including plasma physics, hydrodynamics and physics of the upper atmosphere.