## Journal of Applied Mathematics

### New Exact Solutions of Ion-Acoustic Wave Equations by (${G}^{\prime }/G$)-Expansion Method

#### Abstract

The (${G}^{\prime }/G$)-expansion method is used to study ion-acoustic waves equations in plasma physic for the first time. Many new exact traveling wave solutions of the Schamel equation, Schamel-KdV (S-KdV), and the two-dimensional modified KP (Kadomtsev-Petviashvili) equation with square root nonlinearity are constructed. The traveling wave solutions obtained via this method are expressed by hyperbolic functions, the trigonometric functions, and the rational functions. In addition to solitary waves solutions, a variety of special solutions like kink shaped, antikink shaped, and bell type solitary solutions are obtained when the choice of parameters is taken at special values. Two- and three-dimensional plots are drawn to illustrate the nature of solutions. Moreover, the solution obtained via this method is in good agreement with previously obtained solutions of other researchers.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 810729, 11 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808186

Digital Object Identifier
doi:10.1155/2013/810729

Mathematical Reviews number (MathSciNet)
MR3124606

Zentralblatt MATH identifier
06950889

#### Citation

Taha, Wafaa M.; Noorani, M. S. M.; Hashim, I. New Exact Solutions of Ion-Acoustic Wave Equations by ( ${G}^{\prime }/G$ )-Expansion Method. J. Appl. Math. 2013 (2013), Article ID 810729, 11 pages. doi:10.1155/2013/810729. https://projecteuclid.org/euclid.jam/1394808186

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