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Bifurcations and exact traveling wave solutions of a new two-component system

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Abstract

In this paper, we study the bifurcations and exact traveling wave solutions of a new two-component system from the perspective of the theory of dynamical systems. We obtain all possible bifurcations of phase portraits of the system under various conditions about the parameters associated with the planar dynamical system. Then, we show the existence of traveling wave solutions including solitary waves, periodic waves and periodic blow-up waves, and give their exact expressions. These results can help understand the dynamical behavior of the traveling wave solutions of the system.

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Acknowledgments

This research is supported by the Natural Science Foundation of Fujian Province (No. 2015J05008), and Science and Technology Program (Class A) of the Education Department of Fujian Province (No. JA14023).

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  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, PR China

    Zhenshu Wen

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  1. Zhenshu Wen
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Correspondence to Zhenshu Wen.

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Wen, Z. Bifurcations and exact traveling wave solutions of a new two-component system. Nonlinear Dyn 87, 1917–1922 (2017). https://doi.org/10.1007/s11071-016-3162-x

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