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The mixed interaction of localized, breather, exploding and solitary wave for the (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics

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Abstract

The (3+1)-dimensional Kadomtsev–Petviashvili (KP) equation with weak nonlinearity, dispersion and perturbation can denote the development of the long waves and the surface waves in fluid dynamics. In this paper, the KP equation is illustrated with the symbolic computation. The mixed interaction solutions of local wave, solitary wave, breather wave, exploding wave and periodic wave for the equation are derived by the Hirota method. The effects of dispersion, nonlinearity and other parameters on the interactions are investigated. The solitary wave can be amplified via introducing the local wave. Adjusting the parameters can make the transmission of localized and breather wave more stable. Moreover, a new exploding and periodic wave is observed. It is useful for enriching the dynamic patterns of the wave solutions.

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Acknowledgements

Wenjun Liu and Qin Zhou are contributed equally to this work. The work of Wenjun Liu was supported by the National Natural Science Foundation of China (11674036 and 11875008); Beijing Youth Top-notch Talent Support Program (2017000026833ZK08); Beijing Natural Science Foundation (3182028); Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications, IPOC2019ZZ01); The Fundamental Research Funds for the Central Universities (500419305). This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia, under Grant No. (KEP-64-130-38). The authors, therefore, acknowledge with thanks DSR technical and financial support.

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Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, P. O. Box 122, Beijing, 100876, China

    Weitian Yu & Wenjun Liu

  2. School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Hongxin Zhang

  3. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, China

    Qin Zhou

  4. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL, 35762-7500, USA

    Anjan Biswas

  5. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Anjan Biswas & Abdullah Kamis Alzahrani

  6. Department of Applied Mathematics, National Research Nuclear University, Kashirskoe Shosse, Moscow, 115409, Russian Federation

    Anjan Biswas

  7. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, 0008, South Africa

    Anjan Biswas

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  1. Weitian Yu
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  2. Hongxin Zhang
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  3. Qin Zhou
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Correspondence to Qin Zhou.

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Yu, W., Zhang, H., Zhou, Q. et al. The mixed interaction of localized, breather, exploding and solitary wave for the (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics. Nonlinear Dyn 100, 1611–1619 (2020). https://doi.org/10.1007/s11071-020-05598-3

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