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Fission and annihilation phenomena of breather/rogue waves and interaction phenomena on nonconstant backgrounds for two KP equations

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Abstract

In this paper, we investigate various nonlinear phenomena of two Kadomtsev–Petviashvili (KP) equations. Based on bilinear neural network method, we present the fission and annihilation phenomena of breather waves and rogue waves on non-zero backgrounds of a (3+1)-dimensional KP equation by its reduced equation. Then with the aid of symmetry transformation and Hirota bilinear form, we obtain three interaction solutions on nonconstant backgrounds of a (2+1)-dimensional KP equation with variable coefficients. Also, we perform the analysis of the dynamic characteristics and evolution behaviors of the obtained solutions through three-dimensional animations with proper choices of different values for the parameters. This paper shows that the bilinear neural network method combined with symmetry analysis effectively solves high-dimensional differential equations with constant and variable coefficients.

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Funding

The work is supported by the National Natural Science Foundation of China (Nos. 11902067, 12172086, 12102242).

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Authors and Affiliations

  1. School of Science, Dalian Minzu University, Dalian, 116600, China

    Na Lv, Yichao Yue & Xuegang Yuan

  2. School of Software Technology, Dalian University of Technology, Dalian, 116620, China

    Runfa Zhang

  3. School of Mathematics, Liaoning Normal University, Dalian, 116029, China

    Ran Wang

  4. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Ran Wang

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  1. Na Lv
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Contributions

All authors contributed to the study conception and design. Material preparation, translation, data collection and analysis were performed by Na Lv, Yichao Yue and Ran Wang. Theoretical analysis and algorithm design were performed by Na Lv, Runfa Zhang and Xuegang Yuan. The first draft of the manuscript was written by Na Lv and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Xuegang Yuan.

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Lv, N., Yue, Y., Zhang, R. et al. Fission and annihilation phenomena of breather/rogue waves and interaction phenomena on nonconstant backgrounds for two KP equations. Nonlinear Dyn 111, 10357–10366 (2023). https://doi.org/10.1007/s11071-023-08329-6

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  • DOI: https://doi.org/10.1007/s11071-023-08329-6

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