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A New Composite Technique to Obtain Non-traveling Wave Solutions of the (2+1)-dimensional Extended Variable Coefficients Bogoyavlenskii–Kadomtsev–Petviashvili Equation

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Abstract

In this article, we investigate non-traveling wave solutions for the (2+1)-dimensional extended variable coefficients Bogoyavlenskii–Kadomtsev–Petviashvili equation with time-dependent coefficients (VC-BKP). Inspired by Shang\(^{[24]}\), we apply the extended three-wave method and the generalized variable separation method to the investigated problem for the first time in this article. The technique is effective, easily applicable, and reliable in solving non-traveling wave solutions. We successfully obtain forty-four exact non-traveling solutions, including double periodic solutions, kinky breather wave solution, periodic cross-kink solution and some new exact non-traveling solutions obtained firstly in this paper. These results all have a tail which gives a prediction of physical phenomenon. Moreover, we discuss the arbitrary coefficients of solutions in the real, purely imaginary and complex domains, which greatly enriches the forms of solutions. The dynamic phenomena of four types of exact solutions are demonstrated by contour, 2D and 3D graphics, which help to show their physical interpretation.

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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), Shandong Training Program of Innovation and Entrepreneurship for Undergraduates (No. S202110446093) 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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  2. Lingling Zhao
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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. The figures of the manuscript was drawn by YX. 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. A New Composite Technique to Obtain Non-traveling Wave Solutions of the (2+1)-dimensional Extended Variable Coefficients Bogoyavlenskii–Kadomtsev–Petviashvili Equation. Qual. Theory Dyn. Syst. 22, 83 (2023). https://doi.org/10.1007/s12346-023-00775-2

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