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Extended Jacobin elliptic function method and its applications

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Abstract

An extended Jacobin elliptic function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation that Jacobin elliptic functions satisfy and use its solutions to replace Jacobin elliptic functions in Jacobin elliptic function method. It is interesting that many other methods are special cases of our method. Some illustrative equations are investigated by this means.

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Author information

Correspondence to Huaitang Chen.

Additional information

Huaitang Chen is a doctorate student in Dalian University of Technology. Ever since graduation from Qufu Normal University in 1989, he has been a teacher at Linyi Teachers University. He gained a few prizes in scientific research and the honour of elitist awarded by the gov. He was promoted to associate professor in 1993. His research interests focus on both soliton theory and graph theory.

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Chen, H., Zhang, H. Extended Jacobin elliptic function method and its applications. JAMC 10, 119–130 (2002). https://doi.org/10.1007/BF02936211

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AMS Mathematics Subject Classification

  • 35Q35

Key words and phrases

  • Jacobin elliptic function
  • travelling wave solution
  • shock wave solution
  • periodic solution
  • solution
  • solitary solution