CHINESE JOURNAL OF PHYSICS VOL. 53, NO. 7 December 2015

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53, NO. 7. December 2015. Some New Electrostatic Potential Functions Used to Analyze the Ion-Acoustic. Waves in a Thomas Fermi Plasma with Degenerate ...
CHINESE JOURNAL OF PHYSICS

VOL. 53, NO. 7

December 2015

Some New Electrostatic Potential Functions Used to Analyze the Ion-Acoustic Waves in a Thomas Fermi Plasma with Degenerate Electrons M. G. Hafez,1 R. Sakthivel,2,∗ and M. R. Talukder3 1 Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong-4349, Bangladesh 2 Department of Mathematics, Sungkyunkwan University, Suwon 440-746, South Korea 3 Department of Applied Physics and Electronic Engineering, University of Rajshahi, Rajshahi-6205, Bangladesh (Received April 20, 2015; Revised September 18, 2015) The purpose of this paper is to implement a proposed advanced exp(−φ(ξ))-expansion method to find new electrostatic potential functions that describe the nonlinear propagation of ion-acoustic waves in an ideal plasma with degenerate electrons. The KdV equation is obtained for investigating the ion-acoustic waves in such plasmas by using the reductive perturbation method. The exact traveling wave solutions are established for the KdV equation in the form of hyperbolic, trigonometric, exponential, and rational functions with some free parameters. The influence of the electrostatic nonlinear propagation of ion-acoustic waves has been investigated by considering only hyperbolic function solutions of this equation and different values of the ion to Fermi electrons temperature ratio. The results reveal that the proposed expansion method is a standard, effective, and easily applicable mathematical tool with the aid of computer algebra for solving nonlinear evolution equations arising in plasma physics. The obtained new solutions can be helpful in a proper understanding of the features of small but finite amplitude localized electrostatic ionacoustic solitary waves for astrophysical issues. DOI: 10.6122/CJP.20150921

PACS numbers: 02.30.Jr, 02.70wz, 05.45.Yv

I. INTRODUCTION It is well known that the plasma concept plays an important role due to its important application and potentiality for describing many issues of astrophysical phenomena and space physics. However, it is not particularly easy for research scholars to obtain a qualitative understanding of the basic properties of plasmas. Furthermore in a plasma, one quite frequently encounters non-linear collective effects, which cannot properly be analyzed without difficult mathematical techniques. The nonlinearities in plasma add to the localization of waves, leading to diverse types of important coherent structures, namely, solitary waves, shock waves, vortices, etc., which are important from both the theoretical and experimental point of view. A solitary wave is obtained by a delicate balance between the nonlinear and dispersive effects, which has the permanent profile of a hump or dip shaped nonlinear wave. To make an assessment of this from a soliton, it is noted that a soliton is a special type

*Electronic address: [email protected] http://PSROC.phys.ntu.edu.tw/cjp

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c ⃝ 2015 THE PHYSICAL SOCIETY OF THE REPUBLIC OF CHINA

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