The linear dispersion relation of the dust acoustic wave (DAW) and nonlinear propagation of the dust acoustic solitary waves (DASWs) in the strongly coupled dusty plasma are studied. Under the conditions that a fully ionized three-component model plasma containing electrons, ions, and charge fluctuating positive massive dust grains is considered, and electrons and ions are assumed to obey the Boltzmann density distribution while the inertial dust component is described by a group of classical fluid equations, a linear dispersion relation of DAW is obtained by linearizing the equations of system, and it shown that the dispersion relation of DAW is much influenced by the ion concentration parameter. The Burgers equation describing small amplitude solitary waves is obtained by using the reductive perturbation method. Based on the Burgers equation, the basic features of the DASWs are researched, it shown that the DASW is much modified by the strongly couple effects of the dust grains. The research results may be helpful to understand the properties of localized waves in space dusty plasma.
