磁化尘埃等离子体中的冲击波及其横向扰动稳定性

doi:10.19596/j.cnki.1001-246x.7941

计算物理 ›› 2019, Vol. 36 ›› Issue (6): 682-690.DOI: 10.19596/j.cnki.1001-246x.7941

磁化尘埃等离子体中的冲击波及其横向扰动稳定性

庞军刚^1,2, 宋琳^1,2, 唐娜^1,2, 杨雪滢^1,2, 李晓霖^1,2, 席忠红^1,2,3, 石玉仁^1,2

1. 西北师范大学物理与电子工程学院, 甘肃兰州 730070;
2. 甘肃省原子分子物理与功能材料重点实验室, 甘肃兰州 730070;
3. 甘肃民族师范学院物理与水电工程系, 甘肃合作 747000

收稿日期:2018-08-12 修回日期:2018-11-26 出版日期:2019-11-25 发布日期:2019-11-25
通讯作者: 石玉仁,E-mail:shiyr@nwnu.edu.cn;席忠红,E-mail:zhifuxian@163.com
作者简介:庞军刚(1992-),男,硕士研究生,主要研究领域为非线性物理,E-mail:1773799211@qq.com
基金资助:
国家自然科学基金（11565021，11047010）及西北师范大学青年教师科研能力提升计划项目（NWNU-LKQN-16-3）资助

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

PANG Jungang^1,2, SONG Lin^1,2, TANG Na^1,2, YANG Xueying^1,2, LI Xiaolin^1,2, XI Zhonghong^1,2,3, SHI Yuren^1,2

1. College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, Gansu 730070, China;
2. Key Laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, Lanzhou, Gansu 730070, China;
3. College of Physics and Hydropower Engineering, Gansu Normal University for Nationalities, Hezuo, Gansu 747000, China

Received:2018-08-12 Revised:2018-11-26 Online:2019-11-25 Published:2019-11-25

摘要/Abstract

摘要： 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.

关键词: Zakharov-Kuznetsov-Burgers方程, 动力学稳定性, 线性稳定性分析

Abstract: A class of shock wave solutions of Zakharov-Kuznetsov-Burgers (ZKB) equation is obtained with hyperbolic-function-expansion 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.

Key words: Zakharov-Kuznetsov-Burgers equation, dynamical stability, linear stability analysis

中图分类号:

O411.1

庞军刚, 宋琳, 唐娜, 杨雪滢, 李晓霖, 席忠红, 石玉仁. 磁化尘埃等离子体中的冲击波及其横向扰动稳定性[J]. 计算物理, 2019, 36(6): 682-690.

PANG Jungang, SONG Lin, TANG Na, YANG Xueying, LI Xiaolin, XI Zhonghong, SHI Yuren. Shock Waves in Magnetized Dusty Plasma and Their Dynamical Stability Under Transverse Perturbations[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(6): 682-690.

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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

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