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Multiple rogue wave solutions of the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation

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Abstract

Based on a symbolic computation approach and the Hirota’s bilinear method, the multiple rogue wave solutions of the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation, which can be regarded as a generalization of the generalized rational solutions of Boussinesq equation proposed by Clarkson and Dowie, are constructed. The first-order, second-order, third-order and fourth-order rogue waves are systematically discussed. Moreover, the maximal amplitude and the minimum amplitude of the first-order rogue wave solutions are given. By choosing some specific parameters of these rogue wave solutions, their dynamic behaviors are analyzed.

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Acknowledgements

This work is supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX19_2185) and Postgraduate Research & Practice Innovation Program of China University of Mining and Technology (No. KYCX19_2185)\(^\prime \) and the Fundamental Research Funds for the Central University (No. 2017XKZD11).

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  1. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Wenhao Liu & Yufeng Zhang

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  1. Wenhao Liu
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  2. Yufeng Zhang
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Correspondence to Yufeng Zhang.

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Liu, W., Zhang, Y. Multiple rogue wave solutions of the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation. Z. Angew. Math. Phys. 70, 112 (2019). https://doi.org/10.1007/s00033-019-1159-2

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  • DOI: https://doi.org/10.1007/s00033-019-1159-2

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