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Exact traveling wave solutions and bifurcations of the dual Ito equation

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Abstract

In this paper, we consider the traveling wave solutions for the dual Ito equation. The corresponding traveling wave systems are two singular planar dynamical systems with one and two singular straight lines, respectively. On the basis of the theory of the singular traveling wave systems, we obtain the bifurcations of phase portraits and all possible explicit exact parametric representations of solutions (including solitary wave solutions, periodic cusp wave solutions, smooth periodic wave solutions, compactons, etc.) under different parameter conditions.

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Acknowledgments

This research is partially supported by NSFC grants (11471289, 11162020, 11171309).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, **hua, 321004, Zhejiang, People’s Republic of China

    J. B. Li & F. J. Chen

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  1. J. B. Li
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  2. F. J. Chen
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Correspondence to F. J. Chen.

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Li, J.B., Chen, F.J. Exact traveling wave solutions and bifurcations of the dual Ito equation. Nonlinear Dyn 82, 1537–1550 (2015). https://doi.org/10.1007/s11071-015-2259-y

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  • DOI: https://doi.org/10.1007/s11071-015-2259-y

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