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Equivalence Transformation, Dynamical Analysis and Exact Solutions of Harry-Dym System with Variable Coefficients

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Abstract

In this paper, the combination of equivalence transformation and dynamical system method is performed for Harry-Dym (H-D) system. By means of the improved CK direct method, we give the relationship between the variable coefficients H-D system and the corresponding constant coefficients one. Then, the bifurcation of the nonlinear H-D system is obtained, and the existence of possible solitary wave solutions and some uncountably infinite periodic wave solutions are given by using dynamical system method. Furthermore, the explicit parametric representations of the exact solutions of the system are provided.

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Acknowledgements

We thank the Editor and Reviewers for their constructive comments and suggestions.

Funding

Funding was provided by Natural Science Foundation of Shandong Province (Grant No. ZR2020MA011).

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Authors and Affiliations

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, Shandong, China

    Lina Chang, Hanze Liu, Xuexia Li & Xiangpeng Xin

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  1. Lina Chang
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  2. Hanze Liu
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  3. Xuexia Li
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  4. Xiangpeng Xin
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Correspondence to Hanze Liu.

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This work is supported by the Natural Science Foundation of Shandong Province under Grant No. ZR2020MA011, the high-level personnel foundation of Liaocheng University under Grant Nos. 31805 and 318011613.

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Chang, L., Liu, H., Li, X. et al. Equivalence Transformation, Dynamical Analysis and Exact Solutions of Harry-Dym System with Variable Coefficients. Qual. Theory Dyn. Syst. 20, 29 (2021). https://doi.org/10.1007/s12346-021-00464-y

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  • DOI: https://doi.org/10.1007/s12346-021-00464-y

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