Vasily Yu Belashov
Kazan Federal University, Russia
Title: Dynamics of multidimensional nonlinear wave structures of the soliton and vortex types in dispersive complex media: Theory, simulation and applications
Biography
Biography: Vasily Yu Belashov
Abstract
This paper is devoted to a one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics i.e. the theoretical, analytical and advanced numerical study of the structure and dynamics of two- and three-dimensional solitons and nonlinear waves described by Kadomtsev-Petviashvili, derivative nonlinear Schrodinger classes of equations and also the vortex systems described by Euler-type equations. Special attention is paid to generalizations (relevant to various complex physical media) of these equations, accounting for high-order dispersion corrections, influence of dissipation, instabilities, and stochastic fluctuations of the wave fields. This is consistent representation of the both early known and new original results obtained by author and also some generalizations in theory and numerical simulation of the nonlinear waves, solitons and vortex dynamics in dispersive media. On a level with detail consideration of pure theoretical aspects, special attention is paid to the applications of the theory in different fields of modern physics including plasma physics (such as 2D and 3D ion-acoustic, fast magnetosonic and Alfven nonlinear wave structures and vortex dynamics), hydrodynamics (evolution of 2D nonlinear waves on shallow water with depth varying in space and time) and physics of the upper atmosphere (transformation of 2D internal gravity waves and traveling ionospheric disturbances in regions with sharp gradients of the parameters of medium).