Development of Cnoidal Waves in Positively Charged Dusty Plasmas

The dust-acoustic nonlinear periodic (cnoidal) waves are investigated in a positively charged dusty plasma that interacts with streaming electrons and ions. Different nonlinear evolution equations are derived using the reductive perturbation method, and their cnoidal wave solutions are obtained. The dependence of the dust-acoustic speed and the streaming densities of the ions and electrons on the cnoidal wave profiles are examined. The present model may be of interest to recognize the nonlinear waves in the magnetosphere of Jupiter.