Abstract
Propagation of linear and nonlinear dust-acoustic (DA) waves in an unmagnetized, collisionless dusty plasmas consisting of different size dust grains, two temperature ions, and electrons are investigated, in the case of continuous power law dust size distribution. The standard normal-mode analysis is used to study the stability condition of linear DA waves. For nonlinear DA waves, a reductive perturbation method was employed to obtain a Korteweg-de Vries (KdV) equation for the first-order potential and a linear inhomogeneous KdV equation that accounts for the higher-order nonlinearity and dispersion. A stationary solution for equations resulting from higher order perturbation theory has been found using the renormalization method. The effect of higher-order contributions is also discussed.