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Dynamic properties, Gaussian soliton and chaotic behaviors of general Degasperis–Procesi model

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Abstract

We establish the existences of periodic and soliton solutions to unperturbed general Degasperis–Procesi model, and corresponding solutions are shown to verify it. Especially, the Gaussian solitons are presented, which are barely seen in non-logarithmic equation. Moreover, the stability of soliton and modulation instability of the original equation are analyzed. Finally, by taking the external perturbed terms into consideration, the chaotic behaviors emerge. Corresponding largest Lyapunov exponents and phase portraits are presented to verify our conclusion graphically. The results such as Gaussian soliton solutions and chaotic behavior for the general Degasperis–Procesi model are initially discovered in the present paper.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant no. 42002271 ), and Project funded by China Postdoctoral Science Foundation (Grant no. 2021T140514 ).

Funding

Science Foundation of China, Grant No. 42002271, China Postdoctoral Science Foundation Grant No. 2021T140514.

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Authors and Affiliations

  1. Center of Intelligent Computing and Applied Statistics School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, 201620, China

    Yue Kai

  2. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, 200092, China

    Liuke Huang

  3. Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai, 200092, China

    Liuke Huang

  4. School of Civil Engineering and Geomatics, Southwest Petroleum University, Chengdu, 610500, Sichuan, China

    Liuke Huang

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  1. Yue Kai
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  2. Liuke Huang
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Correspondence to Liuke Huang.

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Kai, Y., Huang, L. Dynamic properties, Gaussian soliton and chaotic behaviors of general Degasperis–Procesi model. Nonlinear Dyn 111, 8687–8700 (2023). https://doi.org/10.1007/s11071-023-08290-4

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