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Lumps and rouge waves for a \((3+1)\)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in fluid mechanics

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Abstract

In this paper, a \((3+1)\)-dimensional variable-coefficient Kadomtsev–Petviashvili equation, which describes the long water waves and small-amplitude surface waves with the weak nonlinearity, weak dispersion and weak perturbation in fluid mechanics, is investigated. Lump, lump–soliton and rouge–soliton solutions are obtained with the aid of symbolic computation. For the lump and soliton, amplitudes are related to the nonlinearity coefficient and dispersion coefficient, while velocities are related to the perturbation coefficients. Fusion and fission phenomena between the lump and soliton are observed, respectively. Graphic analysis shows that: (i) soliton’s amplitude becomes larger after the fusion interaction, and becomes smaller after the fission interaction; (ii) after the interaction, the soliton propagates along the opposite direction to before when any one of the perturbation coefficients is a time-dependent function. For the interactions between the rogue wave and two solitons, the rogue wave splits from one soliton and merges into the other one, and the two solitons exchange the amplitudes through the energy transfer by the rogue wave.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05), and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

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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, Beijing, 100876, China

    Ying Yin, Bo Tian, Han-Peng Chai, Yu-Qiang Yuan & Zhong Du

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  1. Ying Yin
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  2. Bo Tian
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  3. Han-Peng Chai
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  4. Yu-Qiang Yuan
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Correspondence to Bo Tian.

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Yin, Y., Tian, B., Chai, HP. et al. Lumps and rouge waves for a \((3+1)\)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in fluid mechanics. Pramana - J Phys 91, 43 (2018). https://doi.org/10.1007/s12043-018-1609-y

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  • DOI: https://doi.org/10.1007/s12043-018-1609-y

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