Plasma hydrodynamic equations are used to investigate the nonlinear dust-ion-acoustic waves on the lunar dark side that are created by plasma interaction with the Earth's magnetosphere. A plasma system is reduced to one evolution equation, called the Korteweg-de Vries equation. The latter has been solved using the new generalized (G'/G)-expansion method. Different kinds of nonlinear solutions, such as solitary, kink, and periodic solutions, are obtained. The inclusion of plasma quantities in the system significantly affects the nonlinear properties of the DIAWs. The current study holds significance in understanding how Earth's magnetosphere interacts with the lunar dark side. Understanding the dust-ion-acoustic waves on the lunar dark side is important for space physics investigations. The properties of all physical plasma parameters, as well as the nature of the planetary obstacle, determine this nonlinearity. Different analytical solutions of the nonlinear evolution homogenous equation is obtained, which allow for the propagation of all both of solitary, shock-like and periodic pulses. Therefore, sound waves on the dark side of the Moon can support single pulses as well as shock-like and periodic pulses are depending on, the wave propagation plasmas parameter.