A survey of dust acoustic waves (DAWs) in magnetized dusty plasmas composed of negatively or positively charged mobile dust and intertialess quantum electrons as well as ions is presented. The Zakharov-Kuznetsov (ZK) equation is derived via reductive perturbation technique. The solitary wave solution of ZK equation is given and the numerical analysis of the solution with parameters in dust crystals is performed to study the properties of the DAWs with positive or negative dust. The multi-dimensional instability of these solitary waves is investigated via small- k perturbation method. The instability criterion and growth rate relying on obliqueness, the density ratio between ions and dust, the dust cyclotron frequency, the Fermi temperature ratio between electrons and ions, and quantum diffraction parameter are discussed for both cases. The implications of these results to the interior of white dwarf stars and magnetars have been briefly discussed.

中文翻译：

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带正负尘埃的磁化量子等离子体中尘埃声波的多维不稳定性

介绍了由带负电或带正电的移动尘埃和无间隙量子电子以及离子组成的磁化尘埃等离子体中的尘埃声波 (DAW) 的调查。Zakharov-Kuznetsov (ZK) 方程是通过还原微扰技术导出的。给出了ZK方程的孤波解，并对含尘埃晶体参数的解进行数值分析，研究了带正负尘埃的DAW的特性。这些孤立波的多维不稳定性通过小 k 微扰方法进行研究。讨论了依赖倾斜度的不稳定性判据和增长率、离子与尘埃的密度比、尘埃回旋频率、电子与离子的费米温度比以及量子衍射参数。