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Periodic Loop Solutions and Their Limit Forms for the Kudryashov-Sinelshchikov Equation

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  • Bin He
  • Qing Meng
  • Jinhua Zhang
  • Yao Long

Abstract

The Kudryashov-Sinelshchikov equation is studied by using the bifurcation method of dynamical systems and the method of phase portraits analysis. We show that the limit forms of periodic loop solutions contain loop soliton solutions, smooth periodic wave solutions, and periodic cusp wave solutions. Also, some new exact travelling wave solutions are presented through some special phase orbits.

Suggested Citation

  • Bin He & Qing Meng & Jinhua Zhang & Yao Long, 2012. "Periodic Loop Solutions and Their Limit Forms for the Kudryashov-Sinelshchikov Equation," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-10, April.
    • Handle: RePEc:hin:jnlmpe:320163
    DOI: 10.1155/2012/320163
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