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On the Existence of Solitary Wave Solutions for Perturbed Degasperis-Procesi Equation

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Abstract

The Degasperis–Procesi (DP) equation is a significant model of shallow-water waves, which has been well investigated in the current study. Notably, the existence of solitary wave solutions without perturbation has been first proved. However, the persistence of solitary wave solutions of the perturbed DP equation by employing the geometric singular perturbation theory and the Melnikov method has been analyzed. Therefore, the perturbed DP equation possesses a solitary wave solution from the demonstration of having a homoclinic orbit.

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Acknowledgements

The authors wish to express their sincere appreciation to all those who made suggestions for improvements to this paper. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11371326,11975145 and 11901215).

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Authors and Affiliations

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

    Guoan Xu & Yi Zhang

  2. School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, 362021, China

    Guoan Xu

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  1. Guoan Xu
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  2. Yi Zhang
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Correspondence to Yi Zhang.

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Xu, G., Zhang, Y. On the Existence of Solitary Wave Solutions for Perturbed Degasperis-Procesi Equation. Qual. Theory Dyn. Syst. 20, 80 (2021). https://doi.org/10.1007/s12346-021-00519-0

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