Traveling wave solutions using the variational method and the tanh method for nonlinear coupled equations

Kamel Al-Khaled; Mohammed Al-Refai; Ameen Alawneh

doi:10.1016/j.amc.2008.02.009

Traveling wave solutions using the variational method and the tanh method for nonlinear coupled equations

Kamel Al-Khaled^*, Mohammed Al-Refai, Ameen Alawneh

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

This paper applied both the tanh and the He's variational iteration methods for analytic study for the nonlinear coupled Kortewge-de Vries (shortly, KdV) equations. Compared with existing sophisticated approaches, the proposed methods gives more general exact traveling wave solutions without much extra effort. Finally, we present an application to shallow water equations using the two methods, the calculations demonstrate the effectiveness and convenience of the He's variational method for nonlinear coupled equations.

Original language	English
Pages (from-to)	233-242
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	202
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2008.02.009
Publication status	Published - Aug 1 2008
Externally published	Yes

Keywords

Coupled KdV equations
Shallow water equations
Traveling wave solutions
Variational iteration method
tanh method

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2008.02.009

Cite this

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title = "Traveling wave solutions using the variational method and the tanh method for nonlinear coupled equations",

abstract = "This paper applied both the tanh and the He's variational iteration methods for analytic study for the nonlinear coupled Kortewge-de Vries (shortly, KdV) equations. Compared with existing sophisticated approaches, the proposed methods gives more general exact traveling wave solutions without much extra effort. Finally, we present an application to shallow water equations using the two methods, the calculations demonstrate the effectiveness and convenience of the He's variational method for nonlinear coupled equations.",

keywords = "Coupled KdV equations, Shallow water equations, Traveling wave solutions, Variational iteration method, tanh method",

author = "Kamel Al-Khaled and Mohammed Al-Refai and Ameen Alawneh",

year = "2008",

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doi = "10.1016/j.amc.2008.02.009",

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T1 - Traveling wave solutions using the variational method and the tanh method for nonlinear coupled equations

AU - Al-Khaled, Kamel

AU - Al-Refai, Mohammed

AU - Alawneh, Ameen

PY - 2008/8/1

Y1 - 2008/8/1

N2 - This paper applied both the tanh and the He's variational iteration methods for analytic study for the nonlinear coupled Kortewge-de Vries (shortly, KdV) equations. Compared with existing sophisticated approaches, the proposed methods gives more general exact traveling wave solutions without much extra effort. Finally, we present an application to shallow water equations using the two methods, the calculations demonstrate the effectiveness and convenience of the He's variational method for nonlinear coupled equations.

AB - This paper applied both the tanh and the He's variational iteration methods for analytic study for the nonlinear coupled Kortewge-de Vries (shortly, KdV) equations. Compared with existing sophisticated approaches, the proposed methods gives more general exact traveling wave solutions without much extra effort. Finally, we present an application to shallow water equations using the two methods, the calculations demonstrate the effectiveness and convenience of the He's variational method for nonlinear coupled equations.

KW - Coupled KdV equations

KW - Shallow water equations

KW - Traveling wave solutions

KW - Variational iteration method

KW - tanh method

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SN - 0096-3003

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SP - 233

EP - 242

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

Traveling wave solutions using the variational method and the tanh method for nonlinear coupled equations

Abstract

Keywords

ASJC Scopus subject areas

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