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

Hasan Bulut,Seyma Tuluce Demiray

doi:10.3390/mca21020011

Hasan Bulut, Seyma Tuluce Demiray

Open Access

https://doi.org/10.3390/mca21020011

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Journal: Mathematical and Computational Applications	Publication Date: Apr 2, 2016
Citations: 37	License type: CC BY 4.0

Affiliation: Fırat University

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.

Highlights

The survey of new exact solutions for the ion sound wave and the Langmuir wave has a highly important position among the scientists
Many authors have worked on the Langmuir solitons
Degtyarev et al have presented some properties of Langmuir solitons [1]

Summary

Introduction

The survey of new exact solutions for the ion sound wave and the Langmuir wave has a highly important position among the scientists. Many authors have worked on the Langmuir solitons. Degtyarev et al have presented some properties of Langmuir solitons [1]. Benilov has demonstrated the stability of solitons by using the Zakharov equation which identifies the interaction between Langmuir and ion-sound waves [7]. Some authors have focused on Langmuir waves [12,13,14]. Langmuir wave spectral energy densities have been derived from the electric field and compared to the weak turbulence results by Ratcliffe et al [17]. We consider 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 [18]: i

BE Bt

Conclusions