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Novel characteristics of lump and lump–soliton interaction solutions to the generalized variable-coefficient Kadomtsev–Petviashvili equation

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Abstract

With the inhomogeneities of media taken into account, a generalized variable-coefficient Kadomtsev–Petviashvili (vcKP) equation is proposed to model nonlinear waves in fluid mechanics and plasma physics. Based on Hirota bilinear method and symbolic computation, we present lump and lump–soliton interaction solutions of the vcKP equation. These local solutions are derived by taking the auxiliary function as the positive quadratic function or the linear combination of the positive quadratic function and the exponential function. Compared with the results allowed by the constant-coefficient KP equation, lump and lump–soliton solutions for the vcKP equation possess more abundant properties. It is shown that the velocity, moving path, and maximum height of the lump are completely characterized by the time functions rather than the constant parameters. The interaction between a lump and one line soliton are still nonelastic, but the track of the lump obeys the controllable function of time. The lump interacting with resonance soliton pairs exhibits a kind of special rogue wave in which the peak emerges and evolves with the varying path. The detailed analysis and discussion of these solutions are provided and illustrated.

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Acknowledgements

The project is supported by the National Natural Science Foundation of China (Nos. 11705077 and 11775104) and Scientific Research Foundation of the First-Class Discipline of Zhejiang Province (B) (No. 201601).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Hui Xu

  2. Department of Mathematics and Institute of Nonlinear Analysis, Lishui University, Lishui, 323000, China

    Zhengyi Ma & Quanyong Zhu

  3. Department of Photoelectric Engineering, Lishui University, Lishui, 323000, China

    Jinxi Fei

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  1. Hui Xu
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Correspondence to Zhengyi Ma.

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Xu, H., Ma, Z., Fei, J. et al. Novel characteristics of lump and lump–soliton interaction solutions to the generalized variable-coefficient Kadomtsev–Petviashvili equation. Nonlinear Dyn 98, 551–560 (2019). https://doi.org/10.1007/s11071-019-05211-2

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