Dust Ion Acoustic Solitary Structures at the Acoustic Speed in the Presence of Nonthermal Electrons and Isothermal Posit
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ONLINEAR PHENOMENA
Dust Ion Acoustic Solitary Structures at the Acoustic Speed in the Presence of Nonthermal Electrons and Isothermal Positrons1 A. Paula, *, A. Bandyopadhyaya, **, and K. P. Dasb a
b
Department of Mathematics, Jadavpur University, Kolkata, India Department of Applied Mathematics, University of Calcutta, Kolkata, India *e-mail: [email protected] **e-mail: [email protected] Received February 2, 2018; revised May 31, 2018; accepted May 31, 2018
Abstract—The Sagdeev pseudo-potential technique and the analytic theory developed by Das et al. [J. Plasma Phys. 78, 565 (2012)] have been used to investigate the dust ion acoustic solitary structures at the acoustic speed in a collisionless unmagnetized dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions, nonthermal electrons, and isothermal positrons. The present system supports both positive and negative potential solitary waves at the acoustic speed, but the system does not support the coexistence of solitary structures of opposite polarity at the acoustic speed. The system also supports negative potential double layer at the acoustic speed, but does not support positive potential double layer. Although the system supports positive potential supersoliton at the supersonic speed, but there does not exist supersoliton of any polarity at the acoustic speed. Solitary structures have been investigated with the help of compositional parameter spaces and the phase portraits of the dynamical system describing the nonlinear behavior of the dust ion acoustic waves at the acoustic speed. For the case, when there is no positron in the system, there exist negative potential double layer and negative potential supersoliton at the acoustic speed, and, for such case, the mechanism of transition of supersoliton to soliton after the formation of double layer at the acoustic speed has been discussed with the help of phase portraits. The differences between the solitary structures at the acoustic speed and the solitary structures at the supersonic speed have been analyzed with the help of phase portraits. DOI: 10.1134/S1063780X19050088
1. INTRODUCTION The investigations of dust ion acoustic (DIA) solitary structures in four-component electron–positron–ion–dust (e–p–i–d) plasmas have received a great deal of attention in the last few years as e–p–i–d plasma may be found in numerous cosmic sites, such as around the pulsars [1], near the surface of the neutron stars [1, 2], in the hot spots on dust ring in the galactic centre [3], interstellar medium [3–5], interior regions of accretion disks near neutron stars and magnestars [6], in Milky way [5], in the magnetosphere and in the ionosphere of the Earth [7–9], in the magnetosphere of the Jupiter [10] and the Saturn [11], and in laboratory environments [1, 6]. Using the reductive perturbation method, Ghosh and Bharuthram [12] investigated the nonlinear propagation of small but finite-amplitude ion acoustic (IA) solitons and double layers in a collisionless unmagnetized e–p–i–d p
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