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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 810729, 11 pages
Research Article

New Exact Solutions of Ion-Acoustic Wave Equations by ()-Expansion Method

School of Mathematical Sciences, Universiti Kebangsaan Malaysia UKM, 43600 Bangi, Selangor, Malaysia

Received 24 May 2013; Revised 19 September 2013; Accepted 20 September 2013

Academic Editor: Saeid Abbasbandy

Copyright © 2013 Wafaa M. Taha et al. 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.


The ()-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.