Dynamics Of Multidimensional Nonlinear Wave Structures Of The Soliton And Vortex Types In Dispersive Complex Media: Theory, Simulation And Applications | 59532
Journal of Astrophysics & Aerospace Technology
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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
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).
Vasily Yu Belashov has done his PhD (Radiophysics) and Doctor of Science (Physics and Mathematics). His main fields of research are: Theory and numerical simulation of the dynamics of multi-dimensional nonlinear waves, solitons and vortex structures in plasmas and other dispersive media. Currently, he is a Professor at the Kazan Federal University. He was the Coordinator of Studies for the International Program “Solar Terminator” (1987-1992), and took part in Programs WITS/ WAGS and STEP. He is author of 288 publications and one book “Solitary Waves in Dispersive Complex Media”.