Effects of strength of dispersion and dust density on the formation of solitons and shocks in unmagnetized dusty plasma

Abstract

The effects of strength of dispersion on the formation of solitons and shock waves in unmagnetized dusty plasma are studied using reductive perturbative technique. Different relational forms of the strength parameter ε can be chosen to stretch the space and time variables, thereby leading to different types of nonlinearities. The Korteweg–de Vries (KdV) equation for the unmodulated dust acoustic wave is derived and the solitary wave solution is obtained. It is shown that there exists a critical dust density ndc at which the formation of the dust acoustic solitary waves is not possible. Furthermore, the solution of the KdV represents a rarefactive (compressive) solitary wave if nd<ndc (nd>ndc) where nd is the dust density. Using another type of coordinate transformation that reduces the strength of dispersion, the Burgers' equation with shock wave solution is obtained. Shocks with negative (positive) potentials are observed when nd<ndc (nd>ndc), respectively.