On the analytical and numerical solutions of the damped nonplanar Shamel Korteweg–de Vries Burgers equation for modeling nonlinear structures in strongly coupled dusty plasmas: Multistage homotopy perturbation method

Abstract

The dissipative cylindrical and spherical (nonplanar) electrostatic low-frequency dust-acoustic waves (DAWs) including solitary and shock waves in a collisional and unmagnetized strongly coupled dusty plasma are investigated analytically and numerically. The present plasma model consists of inertialess particles including thermal elections and vortex-like positive ions distribution as well as inertial strongly coupled negatively charged dust grains. In the hydrodynamic regime, the fluid governed equations of the present model are reduced to the damped nonplanar Shamel Korteweg–de Vries Burgers (SKVB) equation using the reductive perturbation technique. In the absence of the dissipative effect, the damped nonplanar Shamel Korteweg–de Vries (SKdV) equation is recovered and solved analytically for the first time using a novel analytical approach in order to describe the dynamical mechanism of the dissipative nonplanar dust-acoustic solitary waves. Also, the damped nonplanar SKdV equation is solved numerically using the homotopy perturbation method (HPM) and the hybrid homotopy perturbation method with the moving boundary method which is called multistage HPM (MsHPM). Furthermore, in the presence of the dissipative effect, the damped nonplanar SKdVB equation is solved numerically via the HPM and MsHPM for studying the characteristics of the dissipative nonplanar dust-acoustic solitary and shock waves. For checking the accuracy of the obtained solutions, the maximum global residual error is estimated. Moreover, a comparison between the approximate analytical and numerical solutions is reported. Furthermore, the dependence of dissipative nonplanar structures (solitons and shocks) characteristics on various plasma parameters is examined.