Dust plasma is a new field of physics which has developed rapidly in recent decades.The study of dust plasma has received much\nattention due to its importance in the environment of space and the Earth. Dust acoustic waves are generated because of the inertia\nof dustmass while the restoring force is provided by the thermal pressure of electrons and ions. Since dust acoustic waves were first\nreported theoretically in unmagnetized dust plasma by Rao et al., they have become a research hot spot. In this paper, the excitation\nof dust acoustic waves by a gravity field in a dust plasma is analyzed. According to the control equations of dust plasma motion and\nemploying multiscale analysis and perturbation method, we have obtained a (3+1)-dimensional ZK model. Because of the space\nproperty of dust plasma, (3+1)-dimensional ZK equation is more suitable than KdV equation and (2+1)-dimensional ZK equation\nto describe the real dust acoustic waves.Then, the (3+1)-dimensional time-space fractional ZK (TSF-ZK) equation describing the\nfractal process of nonlinear dust acoustic waves is given for the first time. To further explore how dust acoustic waves change energy\nas they travel, we discuss the conservation laws of the newmodel..............
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