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Japan Journal of Industrial and Applied Mathematics

, Volume 35, Issue 3, pp 1153–1161 | Cite as

An equivalent form for the \(\exp (-\phi (\xi ))\)-expansion method

  • Hong-Zhun LiuEmail author
Original Paper Area 1
  • 173 Downloads

Abstract

Recently, the \(\exp (-\phi (\xi ))\)-expansion method has attracted many authors’ interest. In this article, by making use of a certain Riccati equation, we obtain its equivalent form. Compared with the original \(\exp (-\phi (\xi ))\)-expansion method, the equivalent form is simpler, more direct and facile for application. The nonlinear Gerdjikov–Ivanov equation serves as an example to show its advantages.

Keywords

\(\exp (-\phi (\xi ))\)-expansion Gerdjikov–Ivanov equation Riccati equation Exact solution 

Mathematics Subject Classification

35C07 35Q51 

Notes

Acknowledgements

Many thanks are due to the helpful comments and suggestions from the anonymous referee and support from the Scientific Research Fund of Zhejiang Provincial Education Department (Grant number Y201432746).

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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Zhijiang CollegeZhejiang University of TechnologyShaoxingPeople’s Republic of China

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