Astrophys Space Sci (2015) 357:63 DOI 10.1007/s10509-015-2261-3 ORIGINAL ARTICLE Electrostatic wave structures and their stability analysis in nonextensive magnetised electron-positron-ion plasma T.S. Gill 1 · Parveen Bala 2 · A.S. Bains 3 Received: 2 November 2014 / Accepted: 9 February 2015 © Springer Science+Business Media Dordrecht 2015 Abstract A rigorous theoretical study based on Zakharov Kuznetsov (ZK) equation of ion-acoustic solitary waves (IASWs), their stability analysis in a magnetized e-p-i plasma is presented. The plasma model consists of iner- tial ions, magnetic field, electrons and positrons obeying q -nonextensive velocity distribution. Reductive perturbation method is used to derive ZK equation. The solitary wave structures are dependent on chosen plasma model, whose parameters influence the solitary characteristics. Particu- larly, nonextensivity, proportion of positron concentration, magnetic field and difference between electron and positron temperatures play crucial role in the solitary structures. The present work is also extended to give stability analysis and parametric ranges for the existence of stable and unstable solitons. This research work may be useful to understand the physics of nonlinear electrostatic excitations in different astrophysical and cosmic scenarios like stellar polytropes, hadron matter and quark-gluon plasma. Keywords Zakharov Kuznetsov equation · Ion-acoustic solitary waves · Nonextensivity · Tsallis statistics B T.S. Gill gillsema@yahoo.co.in P. Bala pravi2506@gmail.com A.S. Bains bainsphysics@yahoo.co.in 1 Department of Physics, Guru Nanak Dev University, Amritsar 143005, India 2 Department of Mathematics, Statistics & Physics, Punjab Agricultural University, Ludhiana 141004, India 3 Shandong Provincial Key Laboratory of Optical Astronomy & Solar-Terrestrial Environment, School of Space Science and Physics, Shandong University at Weihai, 264209, Weihai, P.R. China 1 Introduction The electron-positron (e-p) plasmas have been believed to exist in many astrophysical and space environments such as early universe (Ress 1983), active galactic nuclei (Miller and Witta 1987), pulsar magnetosphere (Goldreich and Ju- lian 1969; Michel 1982), solar atmosphere (Goldreich and Julian 1969; Tandberg-Hansen and Emslie 1988), super- nova remnants (Michel 1991), inner regions of the accre- tion disk surrounding black holes (Michel 1982) etc. Also e-p plasma has been produced in laser plasma interac- tion (Zel’divich and Navikov 1998; Shapiro and Teakol- sky 1983) and semiconductor fabrication. The study of e-p plasma is of vital importance in understanding salient fea- tures of Van Allen radiation belts (Lightman 1982; Zdziarski 1988) and some physical processes in tokamak (Surko et al. 1986; Tinkle et al. 1994; Greaves and Surko 1995). The e-p plasma has also been created in laboratory with the help of modern positron trapping technique (Liang et al. 1998). It has been theoretically suggested by Surko and Mur- phy (1990) that annihilation of electron-positron is much larger than the characteristic time scale of the ion-acoustic wave. Recent observations have confirmed the presence of a fraction of ions in astrophysical e-p plasmas (Kotani et al. 1996). Formation of electron-positron-ion (e-p-i ) plas- mas has also been reported in various plasma experiments e.g. laser matter interaction (Zel’divich and Navikov 1998; Shapiro and Teakolsky 1983; Liang et al. 1998), in toka- mak and other magnetic confinement systems (Surko and Murphy 1990; Greaves and Surko 1995), beam plasma ex- periments (Greaves and Surko 1995). Because of long life time of positron, most of astrophysical and laboratory plas- mas become an admixture of electrons, positrons and ions. Therefore, it is worthwhile to study the linear and non- linear wave characteristics in such plasmas. Characteris- tics of wave motion in an e-p-i plasma are quite different