▎ 摘　　要

Graphene can be considered as the material used for many electronic devices. This is due to its excellent physical and chemical properties, which have been studied and implemented from a theoretical basis. The study of graphene-based devices for thermal energy conversion is of great interest. The investigation of the behavior of thermal wave transmission occupied a remarkable area of research in the literature. In these works attention was focused to (1 + 1) dimensional grahene sheet GS, where the governing equation is non autonomous. Here,we construct an extension to the (1 + 1) dimensional thermophoretic waves transmission model equation to (2 + 1) dimensional case. This problem is completely original. The coefficients of the constructed equation are time dependent, so an elaborated method is needed. To this issue, the extended unified method is used to find the exact solutions, in polynomial and rational forms. It is shown that the solutions obtained exhibit a transmission of multi -geometric thermophoretic waves structures, which are new when comparing with those existing in the literature which lumps or wrinkle solitons. Among them, wrinkle chirped, hybrid chirped, complex M-shaped, hybrid-M-shaped, wrinkle solitons, lattice waves, and sink-shape lump waves. Further chaotic termophoretic motion is shown to occur. Also, the effects of thermal conductive coefficients are investigated. Further the stability analysis shows that the TW motion is asymptotically stable.