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Bifurcations and exact traveling wave solutions for the KdV-like equation

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Abstract

Applying the combination of the qualitative theory of differential equation and bifurcation theory of planar dynamical systems to a combined form of KdV-like equation, the bifurcations of phase portraits to the corresponding traveling system of this equation are presented. The exact representations of smooth and non-smooth traveling wave solutions are obtained under different regions of parametric space. Moreover, numerical simulations are provided for some solutions of the equation.

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Acknowledgements

The first author wishes to express his sincere appreciation to all those who made suggestions for improvements to this paper. This research is supported by the NSF-China Grant-11471174 and NSF of Ningbo Grant-2014A610018.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, China

    Zhenli Wang

  2. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, China

    Xiqiang Liu

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  1. Zhenli Wang
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Correspondence to Xiqiang Liu.

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Wang, Z., Liu, X. Bifurcations and exact traveling wave solutions for the KdV-like equation. Nonlinear Dyn 95, 465–477 (2019). https://doi.org/10.1007/s11071-018-4576-4

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  • DOI: https://doi.org/10.1007/s11071-018-4576-4

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