Eur. Phys. J. Plus (2018) 133: 58
https://doi.org/10.1140/epjp/i2018-11873-7

Regular Article

Modulational instability: Conservation laws and bright soliton solution of ion-acoustic waves in electron-positron-ion-dust plasmas

Department of Mathematics, Faculty of Science, Beni-Suef University, 62511, Beni-Suef, Egypt

^* e-mail: ohkalaawy7@gmail.com

Received: 3 August 2017
Accepted: 15 January 2018
Published online: 15 February 2018

Abstract

We consider the nonlinear propagation of non-planar (cylindrical and spherical) ion-acoustic (IA) envelope solitary waves in an unmagnetized plasma consisting of electron-positron-ion-dust plasma with two-electron temperature distributions in the context of the non-extensive statistics. The basic set of fluid equations is reduced to the modified nonlinear Schrödinger (MNLS) equation in cylindrical and spherical geometry by using the reductive perturbation method (RPM). It is found that the nature of the modulational instabilities would be significantly modified due to the effects of the non-extensive and other plasma parameters as well as cylindrical and spherical geometry. Conservation laws of the MNLS equation are obtained by Lie symmetry and multiplier method. A new exact solution (envelope bright soliton) is obtained by the extended homogeneous balance method. Finally, we study the results of this article.