Localized Solitary Waves And Their Dynamical Stabilities In Magnetized Dusty Plasma

Dust plasma is ubiquitous in the universe and laboratories.Since the end of the last century,researchers have been studying dust plasma.There are many frontier research topics on dust plasma,among which researchers have always enjoyed studying nonlinear waves.As far as we know,most work is focused on the transverse stability of line solitons and less work has been done on the properties of the localized solitary waves.A magnetized dust plasma consisting of low and high temperature ions,electrons and dust particles was considered in this paper.The dynamical behaviors can be described by a 3D Zakharov-Kuznetsov equation(ZKE).Interestingly,a type of completely localized solitary waves of ZKE are obtained analytically and approximately for the first time.This kind of solitary wave is also confirmed numerically by the Petviashvili method.In addition,we also analyzed the linear stability as well as the dynamical stability of such solitary waves.The results show that this type of completely localized solitary waves have strong stability.The results of linear stability analysis were consistent with those of nonlinear dynamics evolution.Finally,we numerically studied the collisions between such fully localized solitary waves.The results show that both elastic and inelastic collision exist when two localized solitary waves colliding.The contents of this paper are as follows:Chapter ?,it briefly introduced the background knowledge and development of plasma and dust plasma.Furthermore,both the wave phenomena in dust plasma and dust plasma and the theoretical methods used in the study of these wave phenomena were introduced.The reduction perturbation method was used to obtain the ZK equation describing magnetized dust plasma starting with the nonlinear wave equations describing the plasma system.Chapter ?,it considered magnetized dust plasma composed of low and high temperature ions,electrons and dust particles,whose dynamical behavior could be described by the ZK equation.By the least square method,we obtained the approximate analytical solution of the completely localized solitary waves in the ZK equation.And then,the characteristics of the solution of this kind of completely localized solitary waves.A numerical solution of this class of fully localized solitary waves was obtained by Petviashvili method.Chapter ?,We analyzed the stability of the localized solitary waves of the ZK equation.The Fourier configuration method was used to perform linear stability analysis numerically.Then,a finite difference scheme was constructed to simulate the nonlinear dynamical evolution of the solitary wave.Futhermore,we studied the collision of such completely localized solitary waves.Finally,the main research results were summarized,and the future research work was prospected.