Eur. Phys. J. Plus (2021) 136: 561
https://doi.org/10.1140/epjp/s13360-021-01494-w

Regular Article

Homotopy perturbation and Adomian decomposition methods for modeling the nonplanar structures in a bi-ion ionospheric superthermal plasma

¹ Department of Physics, Faculty of Science, Port Said University, 42521, Port Said, Egypt
² Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, 1988, Al-Baha, Saudi Arabia
³ Theoretical Physics Division, PINSTECH, P. O. Box 45650, Nilore, Islamabad, Pakistan
⁴ PCD, PINSTECH, P. O. Box 45650, Nilore, Islamabad, Pakistan
⁵ Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia

^a samireltantawy@yahoo.com

Received: 14 July 2020
Accepted: 25 April 2021
Published online: 19 May 2021

Abstract

The propagation of cylindrical and spherical (nonplanar) electrostatic ion-acoustic waves (IAWs) in a collisionless, unmagnetized, and homogeneous plasma consisting of hot and cold positive ions as well as superthermal electrons are numerically investigated. The nonplanar Korteweg–de Vries (nKdV) equation is deduced from the fluid equations of the plasma species by employing the reductive perturbation technique. For studying the characteristics of the nonplanar electrostatic IAWs, both homotopy perturbation method (HPM) and Adomian decomposition method (ADM) are devoted for solving the nKdV equation numerically. For checking the accuracy of the obtained solutions, a comparison between the exact analytical solution and the approximate numerical solutions of the integrable case (planar KdV equation) is carried out. Moreover, the absolute error and both minimum and maximum residual errors of both ADM and HPM are estimated. Also, the effect of the physical plasma parameters on the characteristics of (non)planar soliton profiles is investigated. It is found that IAWs are significantly modified due to the presence of excess superthermal electrons and nonplanar geometry.