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

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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.

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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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Authors and Affiliations

  1. Faculty of Science, Nonlinear Science Research Center, Jiangsu University, Zhenjiang, 212013, Jiangsu, People’s Republic of China

    Jiuli Yin, Yanmin Wu, Qianqian Xing & Lixin Tian

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  1. Jiuli Yin
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  2. Yanmin Wu
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  3. Qianqian Xing
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  4. Lixin Tian
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Correspondence to Jiuli Yin.

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Yin, J., Wu, Y., Xing, Q. et al. Limiting behavior and complex dynamics of all solitary waves in the two-component Dullin–Gottwald–Holm equation. Nonlinear Dyn 83, 703–711 (2016). https://doi.org/10.1007/s11071-015-2358-9

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  • DOI: https://doi.org/10.1007/s11071-015-2358-9

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