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Nonlinear Dynamics

, Volume 83, Issue 1–2, pp 703–711 | Cite as

Limiting behavior and complex dynamics of all solitary waves in the two-component Dullin–Gottwald–Holm equation

  • Jiuli Yin
  • Yanmin Wu
  • Qianqian Xing
  • Lixin Tian
Original Paper
  • 172 Downloads

Abstract

All possible exotic and smooth solitary wave solutions to the two-component Dullin–Gottwald–Holm equation are investigated. We classify this equation in specified regions of the parametric space. Moreover, we give the limiting relations of all different solitary waves as the parameters trend to some special values. All solitary waves suffer from external perturbations, and these solutions turn to the chaotic state easily. In view of the variation of the control coefficient, the smooth solitary wave is the easiest one to be controlled into a stable state and the cusped solitary wave is the most difficult to be controlled under the same controller condition.

Keywords

Two component Solitary wave Limiting behavior  Complex dynamics 

Notes

Acknowledgments

This work is supported by the Nature Science Foundation of Jiangsu Province (No. SBK2015021674), and it is also sponsored by Qin Lan Project of Jiangsu Province.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Jiuli Yin
    • 1
  • Yanmin Wu
    • 1
  • Qianqian Xing
    • 1
  • Lixin Tian
    • 1
  1. 1.Faculty of Science, Nonlinear Science Research CenterJiangsu UniversityZhenjiangPeople’s Republic of China

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