Abstract
The propagation of dust ion acoustic waves (DIAWs) for two-temperature ions with isothermal electrons in dusty plasmas has been investigated. Using the reductive perturbation method, the Gardner equation is derived. Many analytical solutions have been presented for small but finite amplitude acoustic waves, e.g. solitary and shocklike waves. The effects of many parameters on the feature of the shocklike waves have been studied for the dusty plasma system. The results of this study could be helpful for understanding the existence of nonlinear potential structures those are observed in various cosmic dust-laden plasmas, such as Saturn's E-ring, noctilucent clouds, Halley's comet and interstellar molecular clouds.