Analytical solitary wave solution of dust ion acoustic waves in nonextensive plasma in the framework of damped forced Ko
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ORIGINAL PAPER
Analytical solitary wave solution of dust ion acoustic waves in nonextensive plasma in the framework of damped forced Korteweg– de Vries–Burgers equation N Paul1*, K K Mondal2, R Ali1,3 and P Chatterjee1 1
Department of Mathematics, Siksha Bhavana, Visva-Bharati, Santiniketan 731235, India
2
Department of Mathematics, Cooch Behar Panchanan Barma University, Cooch Behar 736101, India
3
Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipaul University, Majitar, Rangpo, East Sikkim 737136, India Received: 03 October 2019 / Accepted: 16 September 2020
Abstract: Dust ion acoustic waves (DIAWs) are investigated analytically in the framework of damped forced Korteweg– de Vries–Burgers (DFKdVB) equation in an unmagnetized collisional dusty plasma consisting of negatively charged stationary dust grains, positively charged ions and q-nonextensive distributed electrons. Reductive perturbation technique is used to obtain the DFKdVB equation for DIAWs. The effects of different physical parameters such as the entropic index (q), ratio of unperturbed number densities of electrons and ions ðlÞ, dust ion collision frequency ðmid0 Þ, kinematic viscosity (g0 ), the speed of the traveling wave ðM0 Þ, strength ðf0 Þ and frequency ðxÞ of the external periodic force on the analytical DIAWs are shown. The results of the present paper will be useful in laboratory and space plasmas. Keywords: Solitary wave; Dusty plasmas; Dust ion acoustic waves; Damped forced KdVB equation
1. Introduction Dusty plasma comprises of the neutral particles and charged massive grains other than the usual electrons and ions. It has become the most sought after field of research because of its versatile applications in planetary rings, comet tails, intersteller medium and the lower part of the magnetosphere of the earth atmosphere [1–7]. The presence of the highly charged and massive dust grains in plasma creates several new waves depending on the character and dynamic status of the dust grains. The usual ion acoustic waves (IAWs) modified in the presence of dust grains are called dust ion acoustic waves (DIAWs). Soliton and shock are the fundamental nonlinear coherent structure in the dusty plasma and studied by several authors [8–13]. The study has also been done in the framework of KdV Burger (KdVB) equation where the both dispersion and dissipation terms appear in the equation. Shukla and Mamun [14] derived KdVB equation by Reductive Perturbation Technique (RPT) and investigated the properties of
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solitons and shock waves in strongly coupled unmagnetized dusty plasmas. Using the same technique, Roy et al. [15] analyzed the propagation of IAWs in three component quantum e-p-i plasmas and observed the phenomena of the transition from soliton to shock wave. It was shown that the transition of monotonic to oscillatory shock wave occurs due to the critical composition of electron and ion densities or a critical coefficient of kinematic viscosity at the equilibrium
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