Abstarct: In this study, the properties of dusty plasma and its applications, the behavior of dust particles in a dusty plasma, the forces acting on dust particles in dusty plasma waves (linear and nonlinear) and their dispersion relations is studied. It is shown that the presence of dust particles, causing coupling between the different waves in dusty plasma, which in this thesis are two types of acoustic fashion in a dusty plasma uniform, non-magnetized and has been dealing with weak coupling. Through the Maxwell-Boltzmann distribution equation for the density of electrons and ions and Fourier transform wave dispersion is obtained. After the introduction of linear waves and dispersion equations and results, waves have discussed that domain are sufficiently large so that the non-linear properties can not be ignored. In this section of the fluid equations using the equation Korteweg–de Vries deficit disorder (kdv) have diminished. These equations were solved by changing the independent variables and applying boundary conditions. Suggested solutions to these equations indicate that acoustic and acoustic-ion modes with different domain names for soliton propagation kdv be enhanced. The breadth of the scope of the waves on the plasma parameters σ (ratio of ion temperature to electron), the density of dust particles and quantum agent (H) is studied. Also charged dust particles using dynamic equation in dusty plasma Van der Pol -Mathieu (VDP) solutions derived the equation has a swing that will eventually lead to differential equations, numerical solution using Runge-Kutta method of order 4 was studied and the corresponding graphs.