Solitons dynamics in regions with sharp gradients of basic parameters of propagation medium

2^nd International Conference on Astrophysics and Particle Physics

November 13-15, 2017 San Antonio, USA

Vasily Yu Belashov

Kazan Federal University, Russia

Keynote: J Astrophys Aerospace Technol

Abstract :

We consider the problem of dynamics the multidimensional Solitons which are described by the generalized KadomtsevPetviashvili (GKP) equation in complex continuous media with varying time and/or space dispersive parameters ) ,(, r tf=�?³�?² . This problem is very interesting from the point of view of its evident applications in physics of the real complex media with the dispersion. For example, such situation takes place at propagation of the 2D gravity-capillary waves on surface of shallow water when �?² and �?³ are defined as ( ) ] /3[6/ 2 0 g Hc ρ Ï�?â�?�?=�?² and ] )/3()/()[6/( 2 2 12 12 5 22 0 H ggHHc â�?�? ρÏ�?â�?�?ρÏ�?â�?�?=�?³ respectively, and ρ is the density, Ï�? is the coefficient of surface tension of fluid and ) ,,( y xtHH = is the depth. In this case �?² and �?³ also become the functions of the coordinates and time. Similar situation takes place at evolution of the 3D FMS waves in a plasma in case of the inhomogeneous and/or non-stationary plasma and magnetic field when �?² and �?³ are the functions of the Alfv�?©n velocity vА=f[B(t,r),n(t,r)] and the angle ) ( B kâ�?§=�?¸ , namely: ) /)(cot2/( 22 0 2 ieiA mmcv â�?�?�?¸Ï�?=�?² , )] cot1(cot4)cot/(3[)8/( 2 4224 0 4 �?¸ +�?¸â�?�?�?¸â�?�?Ï�?=�?³ ieiA mmcv . Next interesting example is the dynamics of 2D Solitons of z solar terminator and solar eclipse (SE). In this case dispersive parameters �?² and �?³ are functions of the ionospheric parameters such as electron density, temperature, scale heights for the ions and neutral particles etc. which have sharp gradients in these regions. Here, the problem of study of multidimensional Solitons dynamics ),(, rtf=�?³�?² with was solved in general and for above-mentioned applications.

Biography :

Vasily Yu Belashov is a PhD (Radiophysics), DSci (Physics and Mathematics) holder. His main fields include: Theory and numerical simulation of the dynamics of multi-dimensional nonlinear waves, Solitons and vortex structures in plasmas and other dispersive media. Presently, he is Chief Scientist at the Kazan Federal University. He was Coordinator of studies of the International Program Solar Terminator (1987-1992), and took part in programs like WITS/WAGS and STEP. He is author of 288 publications including 6 monographs.