Wave structures in complex continuous media including atmosphere, hydrosphere and space plasma

Тhe results of theoretical and numerical study of the structure and dynamics of 2D and 3D solitons and nonlinear waves described by the generalized equations of the Belashov – Karpman system (such as the Kadomtsev – Petviashvili and the 3-DNLS classes of equations), and also the vortical systems described by Euler-type equations are presented. The generalizations (relevant to various complex physical media) accounting for high-order dispersion corrections, and dissipation are considered. To study the stability of multidimensional solutions of the equations the method of investigation of the Hamiltonian’s boundness with its deformation conserving momentum of a system by solving the corresponding variation problem is used. As a result, the conditions of existence of the 2D and 3D soliton solutions in the Belashov – Karpman system in dependence on values of the equations’ coefficients, i.e. on the parameters of both the medium and the propagating wave have been obtained. Stability of the 2D- and 3D-vortical systems is studied on the basis of the stability criterions obtained earlier. The evolution and interaction of multidimensional solitons and vortical systems is studied numerically. Special attention is paid to the applications of the theory in different fields of modern physics including plasma physics (FMS, IA and Alfvén waves in space plasma), hydrodynamics (surface waves on «shallow» fluid and the oceanic vortices), and physics of atmosphere (internal gravity waves at heights of the ionosphere F layer, vortices of the cyclonic type and tornados in the Earth atmosphere etc.).