Vasily Yu Belashov
Kazan Federal University, Russia
Title: Evolution of solitary waves in complex media with variable dispersion
Biography
Biography: Vasily Yu Belashov
Abstract
We study the problem of dynamics of the 2D and 3D solitary waves in complex media with the varying time and space dispersive parameters 
. For example, studying of the evolution of the 3D FMS waves in magnetized plasma, which is described by the KP equation 
where 
, 
when b is a function of the Alfvén velocity vÐ=f[B(t,r),n(t,r)] (n is the plasma density) and the angle q: 
. Similar situation has place for the ion-acoustic (IA) waves in collisional dusty plasma when in the absence of dissipation and dust-charge variation the dispersion law are 
where 
is the IA speed in dissipationless plasma with constant-charge dust. It is clear that the dispersion will be variable with variation in time and space of ratio of plasma components (for example, in case of heterogeneous distribution of dust in space). In this case the corresponding equations are similar to that for IA surface waves. We present here the results of numerical simulation of the solitary waves in the KP model distracting from a specific type of medium for different model functions b which are: sharp "break" of 
; 2) gradual change of "height" ; and "oscillations" of 
. As a result we have obtained the different types of stable and unstable solutions including the solutions of the mixed soliton - non-soliton type for different characters of dispersion variations.