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Traveling Wave Solutions of a Generalized Burgers-\(\alpha \beta \) Equation

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Abstract

In this paper, we investigate the bifurcations and exact traveling wave solutions of a generalized Burgers-\(\alpha \beta \) equation. Employing the bifurcation theory of planar dynamical system, we obtain the phase portraits of the corresponding traveling wave system. The existence of the singular straight line \(\phi =c\) leads to the dynamical behavior of solutions with two scales. Corresponding to some special level curves, we give the exact explicit parametric representations of smooth and non-smooth solutions under different parameter conditions, including solitary wave solutions and peakon solutions.

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Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, 321004, Zhejiang, People’s Republic of China

    Wenjing Zhu & Yonghui Xia

  2. Department of Mathematics, China Jiliang University, Hangzhou, 310018, Zhejiang, People’s Republic of China

    Wenjing Zhu

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  1. Wenjing Zhu
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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 the National Natural Science Foundation of China under Grant (No. 11901547, No. 11931016, No. 11671176), Natural Science Foundation of Zhejiang Province under Grant (No. LY20A010016).

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Zhu, W., Xia, Y. Traveling Wave Solutions of a Generalized Burgers-\(\alpha \beta \) Equation. Qual. Theory Dyn. Syst. 21, 23 (2022). https://doi.org/10.1007/s12346-021-00558-7

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  • DOI: https://doi.org/10.1007/s12346-021-00558-7

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