This paper is based on finding the exact solutions for Burger’s equation, Zakharov-Kuznetsov (ZK) equation and Kortewegde vries (KdV) equation by utilizing exponential function method that depends on the series of exponential functions. The exponential function method utilizes the homogeneous balancing principle to find the solutions of nonlinear equations. This method is simple, wide-reaching and helpful for finding the exact solution of nonlinear conformable PDEs.

This paper reports on the synthesis of ZnO nanowires (NWs), as well asthe compound nanostructures of nanoparticles (NPs) and nanowires (NWs+NPs) with different coating layers of NPs on the top of NWs and their integration in dye-sensitized solar cells (DSSCs). In compound nanostructures, NWs offer direct electrical pathways for fast electron transfer, and the NPs of ZnOdispread and fill the interstices between the NWs of ZnO, offering a huge surface area for enough dye anchoring and promoting light harvesting. A significant photocurrent density of 2.64 mA/cm² and energy conversion efficiency of 1.43% was obtained with NWs-based DSSCs. The total solar-to-electric energy conversion efficiency of the NWs+a single layer of NPs was found to be 2.28%, with a short-circuit photocurrent density (J_SC) of 3.02 mA/cm², open-circuit voltage (V_OC) of 0.74 V, and a fill factor (FF) of 0.76, which is 60% higher than that of NWs cells and over 165% higher than NWs+a triple layer of NPs-based DSSCs. The improved performance was obtained due to the increased specific surface area for higher dye anchoring and light harvesting of compound nanostructures with NWs+a single layer of NPs.