The nonlinear propagation of dust acoustic (DA) waves (DAWs) in an unmagnetized electron depleted dusty plasma (containing opposite polarity warm dust grains and non-extensive positive ions) has been theoretically investigated. The nonlinear Schrödinger equation (NLSE) is derived by employing the reductive perturbation method. It is observed that the dusty plasma system under consideration supports two branches of modes, namely, fast and slow DA modes, and that both of these two modes can be modulationally stable or unstable depending on the sign of ratio of the dispersive and nonlinear coefficients of the NLSE. The conditions for the formation of bright and dark envelope solitons as well as the first- and second-order rogue waves have been examined. The numerical analysis has shown that the basic features (viz., stability/instability, amplitude and width of the envelope solitons and rogue structures, etc.) of the DAWs associated with the fast and slow DA modes are significantly modified by dust masses, dust charges, non-extensivity of ions, and other various plasma parameters. The implications of the results to space plasma research (viz., magnetosphere of Jupiter, upper mesosphere, Saturn’s F-ring, cometary tail, etc.) are briefly discussed.

从理论上研究了在未磁化的电子贫化的尘埃等离子体（包含相反极性的热尘埃颗粒和未扩散的正离子）中尘埃声波（DAW）的非线性传播。非线性薛定ding方程（NLSE）是通过采用还原摄动法得出的。可以看出，所考虑的尘土等离子体系统支持两种模式，即快速和慢速DA模式，并且这两种模式根据其色散系数和非线性系数之比的符号可以调制稳定或不稳定。 NLSE。研究了形成明暗包络孤子以及一阶和二阶流氓波的形成条件。数值分析表明，基本特征（即稳定性/不稳定性，与快速和慢速DA模式相关的DAW的包络孤子和无赖结构等的幅度和宽度会被尘埃质量，尘埃电荷，离子的非扩展性以及其他各种等离子体参数显着改变。简要讨论了该结果对空间等离子体研究（即木星的磁层，中层中层，土星的F环，彗星尾等）的影响。