Nonlinear acoustic waves in a collisional self-gravitating dusty plasma

Using the reductive perturbation method, we investigate the small amplitude nonlinear acoustic wave in a collisional self-gravitating dusty plasma. The result shows that the small amplitude dust acoustic wave can be expressed by a modified Korteweg-de Vries equation, and the nonlinear wave is instable because of the collisions between the neutral gas molecules and the charged particles.