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Dynamics of heterotypic soliton, high-order breather, M-lump wave, and multi-wave interaction solutions for a (\(3+1\))-dimensional Kadomtsev–Petviashvili equation

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Abstract

In this study, we investigate a (3+1)-dimensional KP equation, which is widely used to model the behavior of nonlinear waves in plasma physics and fluid mechanics. First, the multi-soliton solutions of the equation are derived using the Hirota bilinear method. Based on the multi-soliton solutions, heterotypic soliton is obtained by setting the partial dispersion coefficient to zero. Under the complex conjugation of the parameters, high-order breather waves are derived. Additionally, the M-lump wave solutions of the equation are derived by applying the long-wave limit. To gain a deeper understanding of its physical dynamics, we conducted numerical simulations to simulate various characteristics of M-lump waves during their propagation, including their peaks, troughs, propagation velocities, and propagation trajectories. Afterward, by combining the long-wave limit with the complex conjugation of the parameters, we discuss three types of multi-wave interaction phenomena described by this equation and illustrate the collision process between waves in graphical form.

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Data Availability Statement

No data were used in this study

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Funding

This project is supported by funding of Visual Computing and Virtual Reality Key Laboratory of Sichuan Province (Grant No.SCVCVR2023.12VS), and Scientific Research Foundation of Engineering and Technical College of Chengdu University of Technology (Grant No. C122022022).

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Authors and Affiliations

  1. The Engineering and Technical College of Chengdu University of Technology, Leshan, 614000, China

    Jie Zhong, Zhimin Ma, Ruoyang Lei, Jiang Liang & Yongli Wang

  2. Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu, 610068, China

    Jie Zhong, Zhimin Ma, Ruoyang Lei, Jiang Liang & Yongli Wang

  3. Southwestern Institute of Physics, Chengdu, 610225, China

    Zhimin Ma

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  1. Jie Zhong
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Contributions

JZ was contributed conceptualization, methodology, and writing-original draft. ZM was performed validation and methodology. RL was involved in software and investigation. JL and YW were attributed software

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Correspondence to Zhimin Ma.

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Zhong, J., Ma, Z., Lei, R. et al. Dynamics of heterotypic soliton, high-order breather, M-lump wave, and multi-wave interaction solutions for a (\(3+1\))-dimensional Kadomtsev–Petviashvili equation. Eur. Phys. J. Plus 139, 289 (2024). https://doi.org/10.1140/epjp/s13360-024-05082-6

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