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Bäcklund transformation, Pfaffian, Wronskian and Grammian solutions to the \((3+1)\)-dimensional generalized Kadomtsev–Petviashvili equation

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Abstract

With the Hirota bilinear method and symbolic computation, we investigate the \((3+1)\)-dimensional generalized Kadomtsev–Petviashvili equation. Based on its bilinear form, the bilinear Bäcklund transformation is constructed, which consists of four equations and five free parameters. The Pfaffian, Wronskian and Grammian form solutions are derived by using the properties of determinant. As an example, the one-, two- and three-soliton solutions are constructed in the context of the Pfaffian, Wronskian and Grammian forms. Moreover, the triangle function solutions are given based on the Pfaffian form solution. A few particular solutions are plotted by choosing the appropriate parameters.

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Acknowledgements

This work is supported by the Fundamental Research Funds for the Central Universities of China (2018RC031), the National Natural Science Foundation of China under Grant No. 71971015, and the Program of the Co-Construction with Beijing Municipal Commission of Education of China (Grant Nos. B19H100010 and B18H100040).

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Authors and Affiliations

  1. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Xue-Jiao He & Xing Lü

  2. Beijing Laboratory of National Economic Security Early-Warning Engineering, Beijing Jiaotong University, Beijing, 100044, China

    Xing Lü & Meng-Gang Li

  3. National Academy of Economic Security, Beijing Jiaotong University, Beijing, 100044, China

    Meng-Gang Li

  4. Beijing Center for Industrial Security and Development Research, Beijing Jiaotong University, Beijing, 100044, China

    Meng-Gang Li

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  1. Xue-Jiao He
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  2. Xing Lü
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Correspondence to Xing Lü or Meng-Gang Li.

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He, XJ., Lü, X. & Li, MG. Bäcklund transformation, Pfaffian, Wronskian and Grammian solutions to the \((3+1)\)-dimensional generalized Kadomtsev–Petviashvili equation. Anal.Math.Phys. 11, 4 (2021). https://doi.org/10.1007/s13324-020-00414-y

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  • DOI: https://doi.org/10.1007/s13324-020-00414-y

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