Shock Waves In Magnetized Dusty Plasma And Their Dynamical Stability Under Transverse Perturbations

Dust plasma plays an important role in understanding different types of collective processes in the universe and laboratory environments,so the propagation of waves in dust plasmas has received much attention.Presence of the charged dust particles in the plasmas not only modifies the wave spectra of plasmas without dust particles,but also introduces certain different eigenmodes,such as dust acoustic waves and dust-ion-acoustic waves.In recent decades,the study of nonlinear wave in plasma has been favored by many researchers.But most of them have been engaged in the study of solitary wave in plasma,a little people have paid attention to the study of shock wave in plasma.We study the wave propagation in the magnetized dust plasma.By the reduced perturbation method,Zakharov-Kuznetsov-Burgers(ZKB)equation describing magnetized dust plasma was derived from nonlinear wave equations in plasma.Theoretical analysis shows that there are two kinds of traveling wave solutions for ZKB equation: oscillatory shock wave and monotonic shock wave.A Class of shock wave solution of ZKB equation is obtained by hyperbolic expansion method.Based on these above,we study the stability of the shock wave solution of ZKB equation.The following are the main work:In the first chapter,we introduce the background of plasma and the phenomena of plasma.In addition,the dust particles in plasma and the electrification process of dust particles are introduced.The second chapter introduces some of the waves that exist in the plasma and the two theoretical methods used in the study of these waves.The reduced perturbation method used in the study of small but finite amplitude DAS waves,and the Sagdeev potential approach used in the study of arbitrary amplitude DAS waves.The third chapter starts with the nonlinear wave equations of plasma,ZKB equation describing magnetized dust plasma is obtained by reduced perturbation method.The monotonic shock wave solution of ZKB equation is obtained by hyperbolic function expansion method,then we analyze the linear stability of the shock wave solution.Numerical results show that the stability of shock wave solution of ZKB equation only depends on the coefficient of dissipation.When the dissipation coefficient is greater than zero,the shock wave solution is stable.When the dissipation coefficient is less than zero,the shock wave solution is unstable.Finally,we construct the finite difference scheme of ZKB equation,we numerically simulate the nonlinear dynamic evolution of the shock wave under disturbance.The numerical results show that the shock wave solution is stable for the positive dissipation.The results of linear stability analysis are consistent with the results of nonlinear dynamics evolution,this indicates that the stability of the shock wave is closely related to the dissipation coefficient.In the finally chapter,we mainly summarize the research results,and also point out the problems left in the work,and look forward to the future research in this field.