Exact Solutions Expressible in Hyperbolic and Jacobi Elliptic Functions of Some Important Equations of Ion-Acoustic Waves

Khater, A. H.; Hassan, Mohamed M.

doi:10.5772/20158

Acoustic Waves - From Microdevices to Helioseismology 2011

DOI: 10.5772/20158

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Exact Solutions Expressible in Hyperbolic and Jacobi Elliptic Functions of Some Important Equations of Ion-Acoustic Waves

A. H. Khater¹,

Mohamed M. Hassan²

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2015

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

Taha

Noorani

Hashim

2013

Journal of Applied Mathematics

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

Taha

Noorani

Hashim

2013

Journal of Applied Mathematics

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EXACT TRAVELLING WAVE SOLUTIONS OF THE SCHAMEL-KORTEWEG-DE VRIES (SCHAMEL-KdV) EQUATION

Yang

Tang²

2015

Jour. Math. Sci. Adv. Appl.

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Exact Solutions Expressible in Hyperbolic and Jacobi Elliptic Functions of Some Important Equations of Ion-Acoustic Waves

Cited by 2 publications

References 55 publications

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

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

EXACT TRAVELLING WAVE SOLUTIONS OF THE SCHAMEL-KORTEWEG-DE VRIES (SCHAMEL-KdV) EQUATION

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