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New type solutions to the (2+1)-dimensional extended Bogoyavlenskii–Kadomtsev–Petviashvili equation calculated via generalized Kudryashov technique

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Abstract

In this paper, we will study solutions of the (2+1)-dimensional extended Bogoyavlenskii–Kadomtsev–Petviashvili (eBKP) equation which describes nonlinear wave propagation in superfluids, plasma physics and fluid dynamics. We successfully apply the generalized Kudryashov technique to obtain many solutions of the eBKP equation. These solutions include not only rational fraction solution, tanh solutions, coth solutions, trigonometric periodic solutions, but also some new elliptic function solutions which are firstly obtained in our paper. Some solutions have linear tails which may explain some physical phenomena. The technique is effective, easily applicable, and reliable in solving such nonlinear problems. Moreover, we give some 3D and 2D graphics to describe the properties of solutions and analyze the effects of linear tails.

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Acknowledgements

The authors would like to express their thanks to the anonymous referee for their valuable remarks and helpful suggestions on the earlier version of the paper.

Funding

This work is supported by the Natural Science Foundation of Shandong Province (No.ZR2020MA013, ZR2023MA002) and National Natural Science Foundation of China (No.12271293).

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Authors and Affiliations

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

    Xiaoxiao Zheng, Lingling Zhao & Yuanqing Xu

  2. School of Mathematics, Faculty of Science, Beijing University of Technology, Ping Le Yuan 100, Beijing, 100124, People’s Republic of China

    Yuanqing Xu

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  1. Xiaoxiao Zheng
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Contributions

The authors have no relevant financial or non-financial interests to disclose. All authors contributed to the study conception and design. Material preparation and analysis were performed by XZ and LZ. The finally draft of the manuscript was written by XZ, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Xiaoxiao Zheng.

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Zheng, X., Zhao, L. & Xu, Y. New type solutions to the (2+1)-dimensional extended Bogoyavlenskii–Kadomtsev–Petviashvili equation calculated via generalized Kudryashov technique. Nonlinear Dyn 112, 1339–1348 (2024). https://doi.org/10.1007/s11071-023-09103-4

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