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N-soliton, M-breather and hybrid solutions of a time-dependent Kadomtsev–Petviashvili equation

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  • Wu, Jianping

Abstract

In this paper, the Hirota bilinear method for the standard Kadomtsev–Petviashvili (KP) equation is extended to a recently proposed time-dependent KP equation. Firstly, general N-soliton solutions of this equation are derived by introducing a new property of the bilinear operator. Secondly, imposing parameter constraints in the N-soliton solutions, M-breather solutions and hybrid ones composed of solitons and breathers are constructed, respectively. Thirdly, by choosing proper time-dependent coefficients, some figures are given to shed light on the dynamic properties of the obtained solutions. These results show that the time-dependent coefficients can bring many different dynamic behaviors, which theoretically indicates that the time-dependent KP equation might be physically important to describe certain phenomena in the nature.

Suggested Citation

  • Wu, Jianping, 2022. "N-soliton, M-breather and hybrid solutions of a time-dependent Kadomtsev–Petviashvili equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 89-96.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:89-96
    DOI: 10.1016/j.matcom.2021.10.025
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