Kinetic theory of nonlinear dust-acoustic waves in a dusty plasma

Using kinetic theory and the reductive perturbation technique, a Korteweg-de Vries (KDV) equation is derived for small, but finite, amplitude dust-acoustic waves in a dusty plasma consisting of electrons, ions and charged dust particles. The analogous equation from the basic set of fluid equations is also derived. Differences between the corresponding stationary solutions are discussed.