磁化尘埃等离子体中的冲击波及其横向扰动稳定性

Shock Waves in Magnetized Dusty Plasma and Their Dynamical Stability Under Transverse Perturbations

利用双曲函数法得到ZKB方程的一组冲击波解,并对波在横向扰动下的动力学稳定性进行研究.对冲击波解进行线性稳定性分析,并构造高精度的有限差分格式求解所得本征值问题.结果表明:对于正耗散的情形,该冲击波在线性意义下稳定;对于负耗散情形,该冲击波在线性意义下不稳定.构造有限差分格式对受扰动的冲击波进行非线性动力学演化,结果表明:对于正耗散的情况,该冲击波是稳定的.

A class of shock wave solutions of Zakharov-Kuznetsov-Burgers(ZKB)equation is obtained with hyperbolic-functionexpansion method.Dynamical stability property of shock waves under transverse perturbations is investigated.Firstly,we made linear stability analysis on shock waves.A finite difference scheme with high accuracy is presented to solve numerically the eigenvalue problem.It shows that the shock waves are linearly stable with positive dissipation,while they are linearly unstable with negative dissipation.Secondly,a finite difference scheme is constructed to make long-time nonlinear dynamical evolution of shock waves.The results show that shock waves of ZKB equation are dynamically stable in the case of positive dissipation.