A realistic multicomponent collisionless complex magnetized dusty plasma system consisting of warm ions, $\kappa $ -distributed positrons and electrons, and immobile dust grains is considered to study the modulational instability (MI) (stable/unstable frequency regimes) of dust-ion-acoustic waves (DIAWs). By employing the reductive perturbation method, a 3-D nonlinear Schrödinger equation (NLSE), which leads to the MI of DIAWs, is derived. Furthermore, the NLSE gives a special type of 3-D rogue wave (RW) solution. It is observed that the spectral index $\kappa $ plays a crucial role on the behavior of DIAWs. The basic properties like amplitude and width of the first- and second-order dust-ion-acoustic RWs are affected by the key complex magneto-plasma configuration parameters, such as spectral index $\kappa $ , temperature ratio, number densities of magneto-plasma species, and ion cyclotron frequency $(\omega _{ci})$ . The implication of our results for space and laboratory plasmas is briefly discussed.

中文翻译：

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电子-正电子-离子-粉尘​​磁化等离子体中的调制不稳定性和粉尘-离子-声学杂波

一个真实的多组分无碰撞复杂磁化尘埃等离子体系统，由热离子组成， $\kappa $ 分布的正电子和电子以及固定的尘埃颗粒被认为是研究尘埃离子声波 (DIAW) 的调制不稳定性 (MI)（稳定/不稳定频率范围）。通过采用还原微扰方法，导出了一个 3-D 非线性薛定谔方程 (NLSE)，它导致了 DIAW 的 MI。此外，NLSE 提供了一种特殊类型的 3-D 流氓波 (RW) 解决方案。观察到光谱指数 $\kappa $ 对 DIAW 的行为起着至关重要的作用。一阶和二阶尘埃离子声学RW的幅度和宽度等基本属性受关键复杂磁等离子体配置参数的影响，例如光谱指数 $\kappa $ 、温度比、磁等离子体物质的数量密度和离子回旋频率 $(\omega _{ci})$ . 简要讨论了我们的结果对空间和实验室等离子体的影响。