Vasily Yu Belashov
The structure, stability and interaction of the multidimensional nonlinear waves and solitons forming on the lowfrequency branch of oscillations in complex dispersive media are studied analytically and numerically on the basis of the nonlinear Belashov-Karpman (BK) system which includes the Kadomtsev-Petviashvili (GKP), the nonlinear schrodinger (NLS) and the derivative nonlinear Schrodinger (DNLS) classes of equations and takes into account the generalizations relevant to various complex physical media including space plasma, atmosphere, hydrosphere and other complex dispersive media, associated with the effects of high-order dispersion corrections, influence of dissipation and instabilities. This is consistent representation of both early known and new original results obtained by authors and also some generalizations in theory of the nonlinear waves and solitons in complex dispersive media. The stability analysis of solutions is based on study of transformational properties of the Hamiltonian of the system. The structure of possible multidimensional solutions is investigated using the methods of qualitative analysis of proper dynamical systems and analysis of the solutions??? asymptotics. The interaction of multidimensional solitons is studied numerically. So, we have considered the nonlinear wave processes in different complex physical media using general approach basing on the general BK system and have obtained the results on dynamics of the 2D and 3D solitons for different physical systems from uniform positions. Some applications of obtained results in plasmas and atmosphere are presented.
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