Motivated by the coming lunar missions, namely Luna-25 and Luna-27, scheduled for landing in the coming years, the investigation of the properties and characteristics of lunar dust, which, in contrast to terrestrial dust, adversely affects technology and creates significant risks to humans. As the Moon orbits Earth, plasma from its surroundings impacts its surface and dust grains above and below; thus, about one-third of the moon's orbit is occupied by the tail magnetosphere, which is thicker and more energetic than the tail regions' very thin plasma. Therefore, investigating the plasma properties in this region is of interest to avoid any unfavorable waves that may affect on the space vessels electronics. For this purpose, we use a three-component plasma fluid model study non-planar nonlinear electrostatic wave modulation on the lunar dark side. A non-planar, nonlinear Schrödinger equation (NLSE) is derived to examine the nonlinear wave envelope, which is produced from the dynamics of lunar negatively charged dust particles, positively charged ions, and Maxwellian electrons. Slow and fast dust-ion acoustic modes exist. The instability region allows the occurrence of nonlinear wave envelopes in the form of rogue waves. The latter are proposed as a physical, temporal, and spatial concentration of energy within a localized wave packet, which is sufficient to establish accumulation particles and influence the overall stability of the environment. The relative ion-to-electron temperature ratio enhances the fast mode's maximum growth rate. The growth rate of modulational instability for the spherical mode is lower than that for the cylindrical mode.
