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Travelling Wave Solutions of the General Regularized Long Wave Equation

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Abstract

In this paper, we study the bifurcation and exact travelling wave solutions of the general regularized long wave (GRLW) equation. Based on the bifurcation theory of dynamical system, the various exact solutions are obtained. We consider the cases: \(p=2n+1\) and \(p=2n\) respectively. It is shown that GRLW equation has extra kink and anti-kink wave solutions when \(p=2n+1\), while it’s not for \(p=2n\).

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Acknowledgements

This work was supported by the Natural Science Foundation of Zhejiang Province under Grant (No. LY20A010016), National Natural Science Foundation of China under Grant (No. 11931016), Fujian Province Young Middle-Aged teachers education scientific research project (No. JT180558 ).

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Authors and Affiliations

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

    Hang Zheng & Yonghui Xia

  2. Department of Mathematics and Computer, Wuyi University, Wuyishan, Fujian, 354300, People’s Republic of China

    Hang Zheng & Luoyi Wu

  3. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, People’s Republic of China

    Yuzhen Bai

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  1. Hang Zheng
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Correspondence to Yonghui Xia.

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Zheng, H., Xia, Y., Bai, Y. et al. Travelling Wave Solutions of the General Regularized Long Wave Equation. Qual. Theory Dyn. Syst. 20, 8 (2021). https://doi.org/10.1007/s12346-020-00442-w

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