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The study of lump solution and interaction phenomenon to (2+1)-dimensional potential Kadomstev–Petviashvili equation

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Abstract

In this paper, we obtained a kind of lump solutions of (2+1)-dimensional potential Kadomstev–Petviashvili equation with the assistance of Mathematica by using the Hirota bilinear method. These resulting lump solutions contain a set of five free parameters and some contour plot with different determinant values are sequentially made to show that the corresponding lump solutions tends to zero when the determinant approaches zero. Then, a completely non-elastic interaction between a lump and a stripe of the (2+1)-dimensional potential Kadomstev–Petviashvili equation is obtained, which shows a lump solution is drowned or swallowed by a stripe soliton.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (11661060) and the Natural Science Foundation of Inner Mongolia Autonomous Region of China (2018LH01013).

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  1. College of Sciences, Inner Mongolia University of Technology, Hohhote, 010051, People’s Republic of China

    Jianqing Lü & Sudao Bilige

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  1. Jianqing Lü
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  2. Sudao Bilige
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Correspondence to Sudao Bilige.

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Lü, J., Bilige, S. The study of lump solution and interaction phenomenon to (2+1)-dimensional potential Kadomstev–Petviashvili equation. Anal.Math.Phys. 9, 1497–1509 (2019). https://doi.org/10.1007/s13324-018-0256-2

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  • DOI: https://doi.org/10.1007/s13324-018-0256-2

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