Exact Traveling Wave Solutions for the  System of Shallow Water Wave Equations and Modified Liouville Equation Using  Extended Jacobian Elliptic Function  Expansion Method

Emad H. M. Zahran; Mostafa M. A. Khater

doi:10.4236/ajcm.2014.45038

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AJCM> Vol.4 No.5, December 2014

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Exact Traveling Wave Solutions for the System of Shallow Water Wave Equations and Modified Liouville Equation Using Extended Jacobian Elliptic Function Expansion Method ()

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DOI: 10.4236/ajcm.2014.45038 3,966 Downloads 4,611 Views Citations

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Emad H. M. Zahran¹, Mostafa M. A. Khater²

Affiliation(s)

¹Department of Mathematical and Physical Engineering, College of Engineering, University of Benha, Shubra, Egypt.
²Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt.

ABSTRACT

In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.

KEYWORDS

Extended Jacobian Elliptic Function Expansion Method, The System of Shallow Water Wave Equations, Modified Liouville Equation, Traveling Wave Solutions, Solitary Wave Solutions

Cite this paper

Zahran, E. and Khater, M. (2014) Exact Traveling Wave Solutions for the System of Shallow Water Wave Equations and Modified Liouville Equation Using Extended Jacobian Elliptic Function Expansion Method. American Journal of Computational Mathematics, 4, 455-463. doi: 10.4236/ajcm.2014.45038.

Conflicts of Interest

The authors declare no conflicts of interest.

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