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

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

Research output: Contribution to journalArticle

13 Citations (Scopus)


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 languageEnglish
Pages (from-to)233-242
Number of pages10
JournalApplied Mathematics and Computation
Issue number1
Publication statusPublished - Aug 1 2008



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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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