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研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布，而大质量的尘埃成分用一组经典流体方程描述，对系统方程进行线性化，得到了尘埃声波的线性色散关系，发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开，得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性，发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。

Dust-acoustic shock waves in strongly coupled dusty plasmas with charge fluctuating positive dust

The linear dispersion relation of the dust acoustic wave (DAW) and nonlinear propagation of the dust acoustic solitary waves (DASWs) in the strongly coupled dusty plasma are studied. Under the conditions that a fully ionized three-component model plasma containing electrons, ions, and charge fluctuating positive massive dust grains is considered, and electrons and ions are assumed to obey the Boltzmann density distribution while the inertial dust component is described by a group of classical fluid equations, a linear dispersion relation of DAW is obtained by linearizing the equations of system, and it shown that the dispersion relation of DAW is much influenced by the ion concentration parameter. The Burgers equation describing small amplitude solitary waves is obtained by using the reductive perturbation method. Based on the Burgers equation, the basic features of the DASWs are researched, it shown that the DASW is much modified by the strongly couple effects of the dust grains. The research results may be helpful to understand the properties of localized waves in space dusty plasma.