New exact solutions of ion-acoustic wave equations by (G′/G)- expansion method

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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.

Original languageEnglish
Article number810729
JournalJournal of Applied Mathematics
Volume2013
DOIs
Publication statusPublished - 2013

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Ion acoustic waves
(G′/G)-expansion Method
Acoustic Waves
Wave equations
Traveling Wave Solutions
Wave equation
Exact Solution
Solitary Solution
Plasma Physics
Kadomtsev-Petviashvili Equation
Hyperbolic function
Circular function
Solitary Wave Solution
KdV Equation
Modified Equations
Kink
Square root
Rational function
Nonlinearity
Three-dimensional

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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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.",
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