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Exact solutions with elastic interactions for the (2 \(+\) 1)-dimensional extended Kadomtsev–Petviashvili equation

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Abstract

In this work, the \((2+1)\)-dimensional extended Kadomtsev–Petviashvili equation, which models the surface waves and internal waves in straits or channels, is investigated via the Hirota bilinear method. N-soliton and high-order breather solutions are obtained analytically. Furthermore, mixed solutions consisting of first-order breathers and solitons are also derived, and the corresponding dynamic behaviors are shown by three-dimensional plots. Additionally, based on the long-wave limit, we obtain line rogue waves, lumps and semi-rational solutions composed of lumps, line rogue waves and solitons. It is noteworthy that the semi-rational solutions derived in this paper exhibit elastic interactions.

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Funding

This work is supported by the NSF of China under Grant No. 11671219, the Natural Science Foundation of Zhejiang Province under Grant No. LY15A010005 and the Natural Science Foundation of Ningbo under Grant No. 2018A610197.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, Zhejiang, People’s Republic of China

    Jutong Guo & Maohua Li

  2. Institute for Advanced Study, Shenzhen University, Shenzhen, 518060, Guangdong, People’s Republic of China

    Jingsong He

  3. Department of Theoretical Physics, Horia Hulubei National Institute for Physics and Nuclear Engineering, 077125, Bucharest-Magurele, Romania

    Dumitru Mihalache

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  1. Jutong Guo
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Correspondence to Jingsong He.

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Guo, J., He, J., Li, M. et al. Exact solutions with elastic interactions for the (2 \(+\) 1)-dimensional extended Kadomtsev–Petviashvili equation. Nonlinear Dyn 101, 2413–2422 (2020). https://doi.org/10.1007/s11071-020-05881-3

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