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The Wronskian and Grammian determinant solutions of a \((3+1)\)-dimensional integrable Kadomtsev–Petviashvili equation

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Abstract

Recently, a new \((3+1)\)-dimensional integrable KP equation is derived from a specific reduction of the \((4+2)\)-dimensional KP equation in Fokas et al. (Fractal Fract 6:425, 2022). We proposed in current paper the Wronskian and Grammian solutions of this \((3+1)\)-dimensional integrable KP equation on the basis of Pl\(\ddot{\textrm{u}}\)cker relation and the Jacobi identity for determinants. Furthermore, three kinds of semi-rational solutions of this equation, namely (i) a hybrid of one lump and one soliton, (ii) a hybrid of multiple lumps and one soliton, and (iii) a hybrid of multiple lumps and multiple solitons are proposed and their novel dynamics are discussed.

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Funding

The work was supported by the National Natural Science Foundation of China (Grant No. 12071304 and No.11871446), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022A1515012554), the Natural Science Foundation of Henan Province (Grant No. 232300420123) and the Doctoral Research Foundation of Nanyang Institute of Technology.

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Authors and Affiliations

  1. School of Mathematics and Science, Nanyang Institute of Technology, Nanyang, 473004, Henan, People’s Republic of China

    Yulei Cao

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

    Jingsong He

  3. School of Mathematical Sciences, USTC, Hefei, 230026, Anhui, People’s Republic of China

    Yi Cheng

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  1. Yulei Cao
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  2. Jingsong He
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  3. Yi Cheng
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Correspondence to Jingsong He.

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Cao, Y., He, J. & Cheng, Y. The Wronskian and Grammian determinant solutions of a \((3+1)\)-dimensional integrable Kadomtsev–Petviashvili equation. Nonlinear Dyn 111, 13391–13398 (2023). https://doi.org/10.1007/s11071-023-08555-y

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