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New exact solutions and related dynamic behaviors of a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

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Abstract

In this paper, a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation is systematically investigated based on the Hirota bilinear method. The explicit N-soliton solution and the bright and dark multi-soliton solutions of it are first derived. Next, various bright and dark higher-order breather solutions, including the periodic line wave solutions, as well as the hybrid solutions composed of solitons, breathers, and periodic line waves, are proposed by virtue of the complex conjugate constraints on the parameters. Then, applying the long wave limit to the N-soliton solution, the bright and dark lump solutions and line rogue wave solutions of the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation are constructed. The semi-rational solutions composed of breathers, lumps, solitons, and line rogue waves are further discussed. These new exact solutions all appear in pairs of bright and dark, which can be interpreted by the uplifts and collapses of energy. In addition, the dynamic behaviors of these exact nonlinear wave solutions are vividly demonstrated by their corresponding three-dimensional diagrams, sectional drawings, and density plots with contours.

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The data that support the findings of this article are available from the corresponding author, upon reasonable request.

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Acknowledgements

This work is supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No.LY24A010002, the National Natural Science Foundation of China under Grant No. 1211153003, the Natural Science Foundation of Ningbo under Grant No. 2023J126, K. C. Wong Magna Fund in Ningbo University.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, Zhejiang, People’s Republic of China

    Lingna Ying & Maohua Li

  2. School of Science, Ningbo University of Technology, Ningbo, 315210, Zhejiang, People’s Republic of China

    Yafeng Shi

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  1. Lingna Ying
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Ying, L., Li, M. & Shi, Y. New exact solutions and related dynamic behaviors of a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09539-2

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