SOLUTIONS OF VARIABLE COEFFICIENTS CKP EQUATION FOR DUSTY PLASMA SYSTEM WITH 𝐺 / 𝐺 - EXPANSION METHOD

By using the reductive perturbation method (RPM), the nonlinear Cylindrical Kadomtsev-Petviashvili (CKP) equation with variable coefficients, for a system of plasma composed of positive and negative dust grains in addition to Maxwellian distributed ions and elections, is derived. With the aid of MATHEMATICA, the 𝐺 / 𝐺 - expansion method is used to analytically solve this CKP equation. New classes of hyperbolic solutions, geometrical solutions, and rational solutions are obtained. The behavior of some of these solutions is graphically presented. At certain conditions, one of the hyperbolic type solutions degenerates into solitary wave solution and the effects of physical parameters on this solitary wave solution are examined. The present study could be helpful to understand the excitation of nonlinear dust-acoustic waves in astrophysical objects such as Saturn rings.