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Math. Comput. Appl. 2016, 21(2), 11; doi:10.3390/mca21020011

New Exact Solutions of the System of Equations for the Ion Sound and Langmuir Waves by ETEM

Department of Mathematics, Firat University, Elazig 23119, Turkey
These authors contributed equally to this work.
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Author to whom correspondence should be addressed.
Academic Editor: Mehmet Pakdemirli
Received: 19 February 2016 / Revised: 26 March 2016 / Accepted: 29 March 2016 / Published: 2 April 2016
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Abstract

This manuscript focuses attention on new exact solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The extended trial equation method (ETEM), which is one of the analytical methods, has been handled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, exact solutions including the rational function solution, traveling wave solution, soliton solution, Jacobi elliptic function solution, hyperbolic function solution and periodic wave solution of this system of equations have been obtained. In addition, by using Mathematica Release 9, some graphical simulations were done to see the behavior of these solutions. View Full-Text
Keywords: the system of equations for the ion sound wave and the Langmuir wave; extended trial equation method; exact solutions; Mathematica Release 9 the system of equations for the ion sound wave and the Langmuir wave; extended trial equation method; exact solutions; Mathematica Release 9
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Tuluce Demiray, S.; Bulut, H. New Exact Solutions of the System of Equations for the Ion Sound and Langmuir Waves by ETEM. Math. Comput. Appl. 2016, 21, 11.

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