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The modified alternative (G'/G)-expansion method to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel'd-Sokolov-Wilson equation.

Akbar MA, Mohd Ali NH, Mohyud-Din ST - Springerplus (2013)

Bottom Line: Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics.In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way.These solutions may be imperative and significant for the explanation of some practical physical phenomena.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh ; School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia.

ABSTRACT
Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.

No MeSH data available.


Solitons corresponding to solutionsu13andv13forp=3,q=2,r=1 andb1=1.
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Related In: Results  -  Collection

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Fig3: Solitons corresponding to solutionsu13andv13forp=3,q=2,r=1 andb1=1.

Mentions: Graph is a powerful tool for communication and describes lucidly the solutions of the problems. Therefore, some graphs of the solutions are given below. The graphs readily have shown the solitary wave form of the solutions (FiguresĀ 1, 2, 3, 4 and 5).Figure 1


The modified alternative (G'/G)-expansion method to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel'd-Sokolov-Wilson equation.

Akbar MA, Mohd Ali NH, Mohyud-Din ST - Springerplus (2013)

Solitons corresponding to solutionsu13andv13forp=3,q=2,r=1 andb1=1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3755786&req=5

Fig3: Solitons corresponding to solutionsu13andv13forp=3,q=2,r=1 andb1=1.
Mentions: Graph is a powerful tool for communication and describes lucidly the solutions of the problems. Therefore, some graphs of the solutions are given below. The graphs readily have shown the solitary wave form of the solutions (FiguresĀ 1, 2, 3, 4 and 5).Figure 1

Bottom Line: Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics.In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way.These solutions may be imperative and significant for the explanation of some practical physical phenomena.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh ; School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia.

ABSTRACT
Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.

No MeSH data available.