On the approximate solutions of a damped nonplanar modified Korteweg–de Vries equation for studying dissipative cylindrical and spherical solitons in plasmas

Abstract

In this work, the effect of both nonplanar (cylindrical and spherical) geometry and the dust-neutral collision on the propagation of dissipative nonplanar electrostatic dust-acoustic solitary waves (DASWs) in a strongly coupled complex plasma (SCCP) is examined. The electrons and ions are assumed to follow a Maxwellian and non-Maxwellian trapped velocity distributions, respectively. The fluid governing equations of the plasma species are reduced to an evolution equation using the reductive perturbation technique (RPT). For describing the dynamical mechanism of the dissipative nonplanar DASWs, the evolution equation (the damped nonplanar Shamel Korteweg–de Vries (SKdV)) is solved numerically using both homotopy perturbation method (HPM) and the improved multistage homotopy perturbation method (MsHPM). The numerical solutions of the integrable planar Shamel-KdV (SKdV) equation using both HPM and MsHPM is compared with the exact solution of the SKdV. Also, the comparison between the numerical solutions of the damped nonplanar SKdV using both HPM and MsHPM is discussed. Moreover, the maximum global residual error for both HPM and MsHPM is estimated for measuring the accuracy of the obtained numerical solutions. Furthermore, the dependence of dissipative nonplanar solitons characteristics on various plasma parameters are investigated.