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New Exact Solutions of Ion‐Acoustic Wave Equations by (G′/G)‐Expansion Method

Author

Listed:
  • Wafaa M. Taha
  • M. S. M. Noorani
  • I. Hashim

Abstract

The (G′/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.

Suggested Citation

  • Wafaa M. Taha & M. S. M. Noorani & I. Hashim, 2013. "New Exact Solutions of Ion‐Acoustic Wave Equations by (G′/G)‐Expansion Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:810729
    DOI: 10.1155/2013/810729
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    References listed on IDEAS

    as
    1. Hasibun Naher & Farah Aini Abdullah, 2012. "New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the (2 + 1)‐Dimensional Evolution Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Hasibun Naher & Farah Aini Abdullah, 2012. "New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the -Dimensional Evolution Equation," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, December.
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