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Traveling Wave Solutions of Generalized Dullin–Gottwald–Holm Equation with Parabolic Law Nonlinearity

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Abstract

With bifurcation method of dynamical system, we investigate the travelling wave solutions of the generalized Dullin–Gottwald–Holm equation (G-DGH) with parabolic law nonlinearity. Based on phase portraits, all possible exact expressions of traveling wave solutions are obtained including compactons, peakons, periodic peakons, periodic wave solutions, solitary wave solutions and kink (or anti-kink) wave solutions. The core of bifurcation analysis is the changes of parameters cause the change of topology of the traveling wave system, and so give different exact solutions. Finally, we summarize our results into a theorem.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Yijian Zhang & Yonghui Xia

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  1. Yijian Zhang
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  2. Yonghui Xia
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Correspondence to Yonghui Xia.

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This work was jointly supported by National College Student Innovation and Entrepreneurship Training Program of China under Grant (No. 201910345019), National Natural Science Foundation of China under Grant (Nos. 11671176, 11931016).

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Zhang, Y., Xia, Y. Traveling Wave Solutions of Generalized Dullin–Gottwald–Holm Equation with Parabolic Law Nonlinearity. Qual. Theory Dyn. Syst. 20, 67 (2021). https://doi.org/10.1007/s12346-021-00503-8

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